Yes, it happened, and all the details are pretty much as you describe. I have seen the photo, but can't find it on the internet.
The preparation was very detailed - it wasn't just a spur of the moment stunt. It also wasn't the first flight through the Arc de Triomphe - someone did it at the end of WW1.
The Eiffel tower has also been flown under. There's a neat video from the cockpit (of a Bonanza)
here.