I have a question. I am a EU citizen, non-French. My husband is from Costa Rica and he can come to EU/Schengen without any visa for 3 months. If we want to move to France for more than 3 months, let's say for around a year, I've read I do no even need to register as an EU citizen. But my husband needs to register, is that right? If he needs to register, will we need to show some rent agreement? Thing is, we are planning to rent AirBnb for long time, but I am not sure if authorities will accept AirBnb reservations as a document/proof of accommodation. Also, we would be there as "not in work", so we will need to prove sufficient funds. Can we prove them via just cash we saved (I believe it is around 800 euros a month), can we just show we have 10K euros in cash or this needs to be deposited to some French bank account?
But my husband needs to register, is that right?
That is correct.
If he needs to register, will we need to show some rent agreement?
Possibly. See Carte de séjour de membre de la famille d'un citoyen de l'Union/EEE/Suisse. As far as I can tell, though, temporary accommodations should be sufficient, including those obtained through AirBnb. Specifically, the page says that you must provide
Indication relative au domicile : apportée par tout moyen
This means that you can use "any means" to show where you will be living.
can we just show we have 10K euros in cash or this needs to be deposited to some French bank account?
The money does not need to be in a French bank account. See Titre de séjour d'un retraité (ou inactif) citoyen UE/EEE/Suisse:
tout document permettant de justifier de la réalité de vos ressources et la durée pendant laquelle vous en disposerez comme des relevés de compte bancaire, des bulletins de pension, etc.
This indicates that you can use bank statements among other documents, but says nothing about where the banks are located. Any bank should be fine, therefore.
However, be careful about the amount. See Séjour de longue durée d'un Européen en France. You may be asked to show slightly more than €10,000 for a year, and rather more indeed if you are over 65, in which case the amount is nearly €17,000 a year for a couple.
Also note that you will have to provide evidence of sufficient health insurance.