When I was forced out of my apartment due to water damage, I stayed in a 2 bedroom apartment in the 4th arrondisement between Bastille and Saint Paul from this company for 1 month:
https://parisnicehome.com/en/apartments/ - it was an ok experience - we had a couple of issues with the apartment, but they were very responsive.
Looking at their site now, however, it doesn't look like they have any 2 bedrooms currently.
I've also tried Paris Attitude. They list a lot of apartments, but they work as a middle man, and so often responses can be slow or even non-existent.