Is “I’ve got an Eiffel Tower, I want to sell you,” a popular or set-phrase used when you heard the story you can’t believe from somebody?

This is a way of saying, "if you believe that, you are gullible enough to believe most anything" (and the speaker should therefore capitalize by making themselves lots of money off of you). Basically, you are so gullible that you are vulnerable out in public. The idea here is that somebody could trick (scam) you by selling something they don't own. Generally something that only a very gullible person would fall for.

Typically (in the USA at least) its either "a bridge", or "The Brooklyn Bridge". However, any large landmark the speaker obviously doesn't own would do as a stand-in.

The landmark in question is often modified to match the situation a bit, just to be cute. In this case, the person in question is French, so the one French landmark a typcial New York Times reader would know about (the Eiffel Tower) was used.

The construction means "If you believe that, then... here's something else to show how gullible you are," but without being quite so blunt about it.

The Eiffel Tower was famously "sold" by "Count" Victor Lustig, a confidence trickster. Wikipedia has a comprehensive account and it's linked in the article to the Frenchman Strauss-Kahn.

Any large monument might be substituted. In the UK it might be London Bridge, because of the commonly-held belief that the American who bought it thought he was buying Tower Bridge.

As usual, it is Dowd being mildly clever. The usual trope in (American) English, is

if you believe that, I've got a bridge I want to sell you

(or minor variations) based on the story (probably a myth) that a common swindle in New York City in the early 1900's was to find someone gullible (who will believe anything you say) and offer to sell them a bridge, usually the Brooklyn Bridge (a marvel of engineering at the time it was built), that is, you'd have to be very gullible to think you could buy a bridge especially one so large and famous as the Brooklyn Bridge.

Dowd is just putting the spin on things by, instead of the Brooklyn Bridge, using a French landmark, the Eiffel Tower, because the subject is about French politics.

Old trope (buying a big bridge) + change in location (France) = very mild joke.