I live in an Asian country and I have planned to apply to PhD positions in France and UK in Pure mathematics.
I wrote to one professor saying that I am interested in his work and would like to work under his supervision for PhD research.
Here is an excerpt from his reply:
"In France we have essentially targeted funding so we need students and advisor to know themselves well in advance so that a project can be defined before applying for funding. It can work only with at least a couple of months preparation before the deadlines for funding applications."
So, there is quite a difference between PhD research in UK and France. In UK the admissions are centralized and other 1st year is taught advanced courses and funding is for 4 years while in France the funding is for 3 years and I don't think there are taught courses, admission is also not centralized.
So, can you please tell me some other differences which I must keep in mind (and which I am unaware of) before writing to professors in France?