I am Irish living in France so have some experience in this area.
First thing you need to know is that France has two kinds of universities; those called universities which are very cheap and comparatively of very poor quality to other universities in the west.
Then there are the Grands Écoles, which are specialized, expensive, excellent and difficult to get into; many French students take two years of prepatory studying before trying to enter them.
What you really need to know is that architecture is almost only taught in these institutions.
This means that you would have to prove yourself to be an excellent student before entering, pay exorbitant fees (5-15K a year) and would not have any time for a job as these institutions work you very hard
So in order to do what you want you would either have to get a bank loan or apply for a scholarship at whichever grand ecole you want to study in.
Also bear in mind that as a non EU citizen your study visa would likely not allow you to work at all.
Yes visa works here, and there are many places you can change money, banks, airports, tourist centres but if you withdrew money here it would automatically come out in euros anyway
Sorry forgot how much university was in America so I suppose those fees to you are very little but they're significant by European standards.
Also even though it won't be cheap or easy I'd still recommend you look it into a bit more because you're right there's nowhere like Paris