Eponine

It would definitely get you on their bad side. So it really comes down to: "does it matter if I'm on their bad side?" If it's a huge public university and a big program (I was at the Sorbonne and most programs accept dozens of students), it should not really matter. If it's a small program, where you've been in direct contact with the profs, and you know the profs have a lot of influence in your field, better not play with fire indeed. If you've heard of extensions being given out before, go for it! Ask very politely and state all your reasons, it might work.

Not gonna lie, I live in Europe and I have never heard of anyone even asking for an extension, exactly for the reason you pointed out. Plus, if they have people on a waitlist, they need to be able to tell them if they got in or not before the deadline. So you're unlikely to get an extension. However, is there any tangible consequence if you accept their offer and then back out if you find a better fit in the US? Usually, European schools ask you to pay a fee to show your commitment. Have they asked for that?

I just sent you a dm!! Feel free to contact me I'd love to talk about this.