Is it common for professors in France/Europe to accept students for PhD positions but ask them to arrange their own funding?
Its certainly normal in the UK. Very few universities fund any PhD students themselves (where would they get the money from?). Most students are funded on government scholarships. How these are awarded varies from field to field and I don't know what the norm is in mathematics. In biology they are awarded to centers called Centers for Doctoral Training (CDT/DTPs), which often cover several universities. Each year professors  compete for the right to recruit a student, which they will then advertise for.
Until now, these scholarships have only been open to &quot;home&quot; students (that is British or EU students). Any overseas students have to obtain a scholarship from their own government, or an NGO or charity of some sort, or pay themselves out of pocket. Most profs will take most students who can bring funding/pay their way.
This year things are changing. CDTs/DTPs will now bed allowed to offer up to a third of their scholarships to overseas students. BUT, they will only pay &quot;home&quot; fees, which are generally less than overseas fees. How this difference is handled is varying from Uni to Uni. Some will say that they will charge full overseas fees to overseas students recruited to these scholarships, and the student would have to find the difference (on the order of £10k a year). Other universities are offering to waive the extra overseas fee.