rental contract

I am in the process of buying an apartment with a sitting tenant which I'll be ok to keep at the existing conditions.

I was then wondering what would be the right procedure concerning the existing rental contract. Should I draw an amendment of the existing contract with the new owner, new bank account where to pay the rent etc. I guess this amendment should be registered too?

I had a look at Code du Logement but there is no detailed procedure in this case.

If you have any experience on this I would appreciate your help.