Is temporary French medical insurance available and recommended

Travel Insurance that offers medical coverage in addition to the usual flight delay and luggage loss will do this for you. Generali Travel Insurance covers medical costs, medical evacuation, repatriation among other coverages, even with their least expensive policy. For destinations like France, for a couple weeks of coverage it will likely be less than $100 per person.

You can't become a member of the national health insurance in France, but you can find insurance that would cover you at Insuremytrip.com or square mouth.com.
Also, some Medicare supplement plans pay for some healthcare outside the US. We always buy trip insurance that covers medical expenses. Sometimes I search on Square Mouth and sometimes on Insure My Trip.
Edit: Since your trip is next month, it's very late to buy insurance due to pre-existing condition and look back clauses. Normally, one buys months out. Please follow Carol's advice and decide if you need medical, or evacuation, or.... AARP has a reduced price for MedJet.

will it be a short visit or an extended stay?

1. Check your regular Medicare supplement insurance or Medicare Advantage insurance to see what coverage you already have.
2. Now check what other coverage you may have, often associated with a credit card. The more "premium" the card, generally the more coverage.
3. Decide which areas of travel insurance coverage you feel like you might need additional coverage for.
4. Look at a website such as insuremytrip to find the sort of coverage that you need. In my case, I feel confident that the coverage I have between Medicare Advantage and my credit card is sufficient for everything except evacuation.

I travel frequently (at least I hope to travel frequently) so I have purchased an annual membership to MedJet for medical evacuation. If you are in a hospital over 150 miles from home, they can provide a medical evacuation to your home hospital if requested by medical team. It gives that extra peace of mind, especially since I am often a solo traveler. I've watched a few of the "testimony" videos on you tube and their newsletters often list some of the costs covered by recent medical evacuations. Often 25,000-60,000 and the insured member pays none of that.

We have an annual travel insurance policy that has medical coverage and evacuation. Our Medigap policy for medicare also covers up to 60K in medical costs (which goes a lot further in Europe -- when I broke my elbow and was hospitalized and had surgery in southern France, the cost was about $4K. It would have been at least 50K in the US for similar treatment -- it was $18K to just have the wires removed in a outpatient procedure a year later. Our travel insurance paid. WE didn't get travel insurance when we were young (we had medical coverage) but now the risks are greater of needing evacuation and that is very costly so we get it now.

You can also get policies that cover ONLY evacuation which is the biggest expense one is likely to encounter; these are annual policies and are renewable up to age 75. We alas have aged out or we would have that and not worry about the rest.

I read about this this international health and evac insurance today in another thread. Excellent coverage for a great price IMO.

https://www.geobluetravelinsurance.com/product_overview.cfm