What is the right time of year to write to professors in France asking for PhD positions?

Question

I am a citizen of an Asian country who completed his master's in math in June 2020. I wanted to study more topics before applying for a PhD (in one of the pure mathematics subjects) in Europe, but got ill in Jan 2021, and couldn't apply to a single grad school.

But I did write to some professors, and in Jan 2021, one professor in France replied the following:

We essentially have targeted funding so we need student 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 couple of months preparation before the deadlines of funding applications.

Question: In which month of the year should I start writing to professors in France asking if they are willing to supervise me for a thesis, so that I can get funded (as my country doesn't offer any financial assistance for students studying abroad), and so that deadlines are not missed.

Edit: I also want to tell that although I tried my best to ask professors and take their guidance (in my university from which I did my master's), I wasn't helped much despite having good grades and really good knowledge of the branch I want to pursue a PhD in. The research and general academic environment is not so good and that is one of the reasons I want to go abroad for further studies.

Thank You!!

Answer 1

Question: In which month of the year should I start writing to professors in France asking if they are willing to supervise me for a thesis, so that I can get funded (as my country doesn't offer any financial assistance for students studying abroad), and so that deadlines are not missed.

Any month. Firstly, different funding sources have different deadlines. Secondly, different professors are busy at different times. Some may be able to make time available on short notice, others will need to plan many months ahead to schedule time for defining a project. Some funding sources require that money starts to be spent immediately, others may allow a time window for when the PhD candidate starts. PhD candidates may not necessarily need to start at the beginning of the academic year, either.