Looks like the Eiffel Tower's steelwork was primed with the old "red lead"- basically lead oxide and linseed oil with some Japan drier. Greatest primer for outdoor steelwork, not used in the USA due to the lead content. Between the old steels seeming to have much better corrosion resistance and the red lead primer (and probably years of lead-based top-coat paints), the Eiffel Tower is unlikely to have too many corrosion issues. The places to watch on old riveted structures are the connections, as is shown in the second photo that Paul39 posted. A common occurance in these types of riveted built-up connections is known as "rust pack out". If water gets in between the various layers of steel in this type of connection and starts corrosion at the interface, it is a failure mechanism. The rust can create enough expansive force to break rivets in tension. The rivets are already stressed from the shrinkage when they cool after being driven. Add some additional tensile stress from rust pack out and rivets can fail. Since the rivets are "upset" in their holes in the steel structural members, rivets which fail in tension usually do not fall out of the connection. Visual inspection is misleading, since all rivets will appear in place. The only real way to properly inspect exposed riveted structures is to climb the steel and sound each and every rivet with a hammer. Unfortunately, in today's world, this method is not used too much. In the USA, many older bridges with countless rivets and riveted connections are not given the thorough inspection they should be getting. The method is to put the inspectors out and along the steel using a "snorkel" type of bucket truck made for bridge inspection, and to check a "representative sampling" of the connections. Whether the new generations of bridge inspectors even sound the rivets on the "representative sampling" of connections is something I wonder about. They may go with a visual inspection or possibly apply ultrasonic testing to the rivet heads, hoping to get the UT beam to go down thru the shank to the opposite head and bounce back if the rivet is sound.
Painting the Eiffel Tower is one of those endless jobs, perhaps the stuff of urban legends. The kind of job that, when the paint crew reaches the end of the job, it's time to go back and start again. I suspect the Eiffel Tower steel is painted mainly by using brushes, with the painters scaling off any loose paint as they go along.
Somewhere in the past, I read that Gustave Eiffel, when he designed the tower, realized he was into uncharted waters in many areas. One was dealing with winds aloft, and another area was getting workmen who would be comfortable working at the heights the tower would reach. The tower was one of the very first high steel structures, and if I recall correctly, was supposed to be only a temporary thing for some sort of trade fair or exposition.
At the time the tower was erected, I wonder if compressed air riveting guns were in use. Obviously, as many connections as possible would be "shop riveted" using a hydraulic riveter (known as "power driving", a "C frame riveter" or a "bull riveter"). There would still be countless field riveted connections to be made in the erecting of the tower. If compressed air riveting guns were not in use, the thought of men swinging riveting hammers up on the tower is hard to imagine.
I visited Paris with my parents in 1965, and we did go up on the tower as far as the public was allowed, using the elevators. 1965 was a good time to see Europe. It had not gotten ridiculously over-run with tourists, no terrorist acts were occurring, and my parents figured the trip using a book called "Europe on 5 dollars a day". We travelled 2nd class on trains, took busses, and had a wonderful family vacation. Somewhere along the line, my mother read about taking a "Tour of the Sewer" in Paris. The tour was of a storm sewer rather than a sanitary sewer. The entry for the tour occurred at a manhole (what else) in the middle of a street, allegedly on the spot where Marie Antoinette was guillotined. Sewer workers wearing high leather boots and dressed in blue work clothes arrived with carbide lamps and opened the manhole and put up a traffic barrier. We went down a flight of stone stairs, apparently hewn out of limestone. At the base of the stair was what amounted to a canal, with two footways alongside it. The sewer was a horse-shoe shaped tunnel, with the two narrow footways above the water level. In the channel there was a steel barge about 30 feet long moored there. One elderly sewer worker got up on the stern end of the barge and took the tiller. He turned on two big sealed beam lamps powered with a storage battery, which really helped see things down there. His cohorts undid the mooring lines and took hold of them, holding the barge back from being swept along too fast- and into the River Seine. The oldtimer at the tiller began to spiel in French, which my parents knew enough of to translate for us. Mainly, he was showing us where branches of the sewer entered the main branch we were on, and telling us about activities of the French resistance in WWII using the sewers for their operations, and how SS men disappeared via the sewer. The carbide lamps were hissing away, throwing their light, the sealed beam lamps seemed to be piercing a mist or fog, and the roar of water got louder as the steel barge neared the River Seine. Soon enough, the sewer crew snubbed off the lines to bitts set in the stone work. End of the tour. The crew was not going to haul a barge load or people back against the current in the sewer. We came up via another manhole, having no idea where in Paris we were. My parents figured it out soon enough and we got on with our exploration of Paris. We stayed in a pension (Hotel du Nil, 10 Rue le Helder). My parents made us kids memorize where we were staying in case we got separated, and 55 years later, I can still recite the pension's name and address. My father was a WWII US Army veteran, and he had been in Paris after the liberation. He had been wounded and was evacuated to a hospital in Paris, where he underwent an operation to try to fuse his right ankle and repair some damage to his right shoulder. Dad remembered walking around Paris with a cane. He also remembered being billeted with civilians in Soissons (sp ?) and had fond memories of time spent with various French families. In 1965, it seemed like we could walk into museums without waiting on any lines, let alone any security measures. My mother used to say we were fortunate in seeing Europe while it was still "unspoiled".
We left Paris to go to Nice using a fast night train called "le Mistral". In 1965, the French National Railways was still running plenty of steam locomotives. When we got to the Gare du Nord, it seemed most of Paris was at the station, probably the national vacation time and the time French Army reserve units went on maneuvers. It seemed like anything that could roll was at the station, including numerous steam locomotives. My folks taught me how to ask to get up in an engine cab in French, translating steam locomotive into "horse of iron" if I remember right. I was allowed to get up in the cab of a French steam locomotive for a few minutes. We had arrived at the station early, so checked our baggage. Dad and Mom then took us to a "Brasserie" (if I spelled it right) across a side street from the station. It was a workingman's kind of bar. We ordered sandwiches, and although I was not even 15, Dad bought me a beer. About that same time, an older French railwayman came into the barroom. He had a prosthetic leg which looked like something he or his friends had made in the railway shops- turned from aluminum bar stock, kind of like a table leg with some ornamental design to it and a big hard rubber puck at the bottom end of it. He wore the usual blue work clothes and a lantern hung off his belt. A woman who was quite obviously "a lady of the evening" was at the bar and evidently knew the old railroader. She got them both a drink and they went to the juke box. She punched a record of a "Chanteuse" singing and the old railroader put his arm around her waist. Prosthetic leg and lantern, he was dancing with the lady and holding a drink in his hand. I had my beer, and felt like I was about 10 feet tall, drinking with Dad and the French railroaders and all else. We saw the Louvre, went to a number of sites including Versailles, but I think my experience with the French railroaders was the highlight of my time in Paris. That night, we boarded the Mistral and got in a sleeping compartment which we shared with a French couple. The Mistral left the station, and I remember seeing a woman living along the tracks turning the blower on a small forge to grill her family's supper. The Mistral soon was highballing. I could not fall to sleep, and quickly realized we were passing numerous freights and local trains, many with steam locomotives, that had gone onto sidings to let the Mistral highball through. I got up and walked to the end of the coach we were in, and found the access door had an upper half which could be opened independently of the bottom half (which would have likely dropped the deckplate out from under me and opened the "trap" with the access steps). I opened the top half of the entry door and hung out, looking into the cabs of steam locomotives as we roared past, and seeing endless trains of dead steam locomotives heading as scrap to the Ruhr, in Germany. There were destination signs on those trains of dead locomotives, and from time to time, I was able to make them out. I have no idea how long I was looking out the entry door at the sidetracked trains and night landscape. Mom came padding down the corridor and found me, asking what I was up to. I told her. She told me about living on the farm when she was a girl, and how the sound of steam locomotive whistles used to carry far on winter nights, so she'd hear it while laying in bed. She told me how the whistles told her of a world beyond the farm and how she had dreamed of seeing more of it. So, Mom and I stood there for another long while with the wind blasting at us through the opened door and me looking at sidetracked steam locomotives in the night. Mom made it to 100 years of age, had her wits about her to the end, and used to fondly recall that experience on Le Mistral with me. I could not tell you too much else about our trip to Paris, but then, a kid with his head wrapped around machinery and locomotives was not going to pay much attention to great works of art or department stores, and I was too young to go to the Follies (something my old man spoke of).