Studying mathematics abroad - specifically France
The French system is a bit weird. The best places to go are not the university, but the so-called «grandes écoles». So if you want the best, you should go to either the Ecole Normale Supérieure of Paris, or the the Ecole Normale Supérieure of Lyon, or the Ecole Normale Supérieure of Cachan or the Ecole Polytechnique. Beware that the selection level is quite high.
Now the second best places to go are big universities, which are not so bad. I recommend Jussieu (Université Paris 7), or Chevaleret (Paris 6). The main difference is that there is almost no selection at the first year undergrad level, whereas for the «grandes écoles» the selection is a huge national exam 2 years after high school... (you have to be in the first 200 out of several thousands to be in the ones I mentioned).
Hope that helps ! You should come, France is a nice country to study in ! =)
I came to France to study after my bachelor's (which I did in Iceland). So far I've done my master's here and am finishing my PhD. I've spent my time here at the university in Grenoble.
I mostly concur with Glougloubarbaki. If your main objective is to study math, then try to go to a grande école, or go directly to a "Master 2" in a public university. This is the second year of masters, where you start specializing. The difference in dedication and skills of the students in public universities vs. grands écoles levels out during the M2.
If you want to take some time to see more of the culture and the country, then do the first year of master's in a public university as well, but know that if your background is strong you won't profit much from it.
As was already said, it is non-trivial to get into a grand école, but I recommend you try. You have about a 90% chance to get into any public university you want. I suspect the 10% failure rate is mostly due to papers getting lost along the way.
With these caveats in place, the question of which university to go to starts to depend an awful lot on what field you want to study for your masters. Different universities have different research groups. Paris has the advantage of having a lot of maths departments, so there is choice there, but other cities have good groups as well. For example, Grenoble has active groups in topology and algebraic geometry, some good analysis is coming out of Toulouse, etc. We might be able to give you some more detailed pointers if you tell us what you're interested in.
French system is unique regarding other countries in that fact that it is generally considered as a shame and a disgrace for a student to enter at 1st year of French public universities. This means that this student has failed to all the 'Grandes Ecoles' entry tests (Big Schools) but also to all the less prestigious engineering schools and the technology institutes - which are really like a thousands -
The paradox is that the teachers in these public universities come often themselves from the Elite Grandes Ecoles.
The other paradox is that a great deal of very good mathematician and scientists comes from public University despite this bad reputation.
For example Grothendieck did not come from the Ecole Normale Superieure but directly from the university of Montpellier.
At Phd level , students from Grandes Ecoles often enter directly public University.
Note that the mathematics taught at Msc level in Parisian Universities are often themselves quite good.
The French system is based on a sort of cruel and hard elitism which ages from Napoleon !st and most of the Grandes Ecoles do not provide Mathematicians but Engineers. Almost all Elite French Mathematicians come from one only ultra-selective school which is the Ecole Normale Superieure of Ulm.
This system seems a bit outdated by now and frankly a bit stupid ( I am from one of the top Grandes Ecoles myself )
With regards to the U.S system, the U.S system is for me unable to produce mathematicians on their ground, they need to constantly import them either from India, China, Russia or even France.
I wish we all could be like Grothendieck!