This is the sort of thread I found very useful when we planned our move to France, so I’m typing this here as opposed to a private message. Apologies for the length!
Okay, so dealing with actual practicalities first, you already know that being an EU resident you don’t need to worry about visa etc. Your husband having an EU spouse is entitled to a carte de sejour (CDS) which is his permission to stay. This will involve several trips to the local prefecture to queue/apply etc. There will be certain papers he needs to put together, some of which should be gathered whilst you are still in the UK, for eg certified copies of his birth certificate and your wedding certificate; for your child you should obtain for them a copy of the certificate if born in the UK. I’m not sure what country you’re from, but many EU countries can issue an ‘act of birth’ certificate which is often in the home language and also in French (I got one for my son who was born in the UK but his father is EU).
Health - French healthcare system is excellent (so much so that husband didn’t get private healthcare included as part of the French contract). Appointments for doctor/dentist/pharmacy can be booked online via Doctolib app, even before you have your Carte Vitale. You will need a French bank account to apply for your CV. Your child can go on your card. Your husband will need to apply for his once he has his account and also his CDS.
Does your husband have settled status in the UK? If so, he’s still entitled to NHS treatment, as long as you don’t stay away more than 5 years.
Tax - as you say, you won’t get double taxed (that only happens after you’ve been in France for five years) so the tax situation is not going to be an issue.
A bank account can be opened up really quickly; I got mine opened within a couple of days of having moved to our rented property. You do need an address, so your idea of basing yourself in an Airbnb is not a bad idea, especially to start with. I opened mine with Credit Agricole Brit line, which is specifically for English-speaking people and it’s very easy. In the meantime Starling bank is a UK phone/app-based bank; you can open an account within half an hour and they have a very handy euro section where you use your phone contactless app to pay for things in euros even before a debit card arrives (absolute lifesaver for me for the first couple of weeks). Apply for this whilst still in UK so that you have the debit card (which you can use to pay for things in both £ and €). Fees are very low for converting £ to € and there are no subsequent fees for paying in €.
On to the less practical side by very important friendships etc …
People are right to say that you won’t pick up much French during the amount of time you’re planning to be there. You’ll get a little bit by watching TV, going to supermarket/going out for dinner etc, but not really much more than that. Your child will start school at three years (maternelle) so she will pick up some French. In fact it’s a good age for her to learn French but unless you keep it up when you return to the UK, she’s not really going to maintain it. You might meet some parents at the school gates perhaps if your child makes friends, but a lot of French parents work, and you’ll notice a lot of nannies around (plenty of Chinese nannies here in Paris). The friends I’ve met so far have mostly been expat; it’s just the way it is. Facebook groups are your friend. Search for ones in the areas you’re interested in, and ask questions. That is where I got my initial info from.
Talking of towns, bear in mind the logistics. I am in the western suburbs of Paris and it’s lovely; very handy for central Paris for my husband and best of all the Eurostar back to London is so much more convenient than having to fly. Paris also has a lot of activities and groups, particularly during school holidays. French parents believe in lots of activities and holiday clubs (stages) abound, often starting at 3yrs.
If you don’t want to be lonely, I do suggest you look for towns with expat communities/international schools/active English-speaking Facebook groups. I’ve met some nice French women, but they too are expats whose children are at the international schools. Realistically you’ll be looking for women who don’t work and who are free in daytime for meet ups and play dates.
To summarise, it’s doable, as long as you treat it as an adventure and a chance to experience another lifestyle/culture, and choose the area carefully.