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.