Unfortunately, I do not know how the probation period works in France. At least in Spain, They can fire you without motive. When I was relocated to Spain, I asked to work remotely because of this. When all the visa paperwork was done, my probation period had ended.

I think op was under probation period.

Based on my experience, the ideal scenario is living in a neutral country.

I relocated to Barcelona with 1 dog and two cats. It was not easy to find an apartment but not impossible.