It is unlikely.
If you move away from France, the fact of keeping a second home or rental property does not give you any special status.
A Carte Vitale is mostly for people affiliated to the French social security system on the basis of residency in France.
They may also be held by retirees living in France but affiliated to another EU country’s social security and who can obtain a Carte Vitale via the S1 form system when they move to France.
Britons currently in France will retain this right under the Withdrawal Agreement if the UK leaves the EU with a deal.
There are a few exceptions where someone may be living outside France but still have one.
Retirees of French pension schemes who move abroad may retain a French Carte Vitale to use on trips back to France.
Another case would be someone affiliated to French social security who goes abroad in the EU to work as a travailleur détaché (posted worker).
Send your queries about life in France by email to firstname.lastname@example.org