Why, historically, were there many notable French mathematicians in the 18th and 19th centuries? A conversation recently came up as to why specific cultures have excelled in certain fields, or why many influential people in a time period came from one nation. 
It would seem that much of the fundamental math taught at the secondary and undergraduate level was discovered by French people. What are the cultural/political reasons for this to be the case? Why were French schools at the time so strong in mathematics? Why specifically French?
 A: "The fact that Paris was the most prestigious university in the world at the time surely did not reduce the amount of French mathematicians, and the fact that France had (likely) the largest and wealthiest population in Europe is also beneficial, but I believe there is something more fundamental at play here - sample bias. The aforementioned reasons may answer your question satisfactorily, and there may not actually be a sample bias - I do not have access to enough statistics to argue definitively after this point. You may wish to stop here, as anything beyond will be "purely" based on opinion mixed with some facts.
You chose 10 or so large names, all of whom were French. That's great! However, the timescale is vast. You seemingly define "after the Renaissance" to be anywhere between 1500-1900. Any European country had big mathematicians in that timescale.
To show how the list is biased, consider Euler and (Carl Friedrich, that's my bias) Gauss - the second greatest and greatest mathematicians, respectively. One was Swiss, the other German. Then consider the following list:
Lagrange was Italian.
Weierstrass was German.
Mittag-Leffler was Swedish.
Newton was English.
Taylor was English.
MacLaurin was English.
Leibniz was German.
Green was English.
Lorentz was Dutch."
-Carl-Fredrik Brodda
