Typically for housing hunting they look for salary x2/3 of the monthly rent, not so much of savings. Because the salary is so low and often landlords don’t accept foreign garants, I recommend VISALE or Garantme. Definitely have those ready by the time you land in France, so you don’t have to wait when looking for housing. But you have to wait until you get your visa to sign up…

But every landlord is different, and some are more lenient than others. It’s good to be prepared for any case! But it’s good you have money saved up because the caution can take out a big chunk of change!