In general, you'll need health insurance that covers you for your duration in France. You will need to show proof of this insurance at the time you apply for the visa at the French consulate closest to your home. Since your wife is French, however, you will apply for a family visa rather than a short/long stay tourist visa. Within two months of arriving in France, you'll go to the préfecture with your wife and the visa in your passport to get your 'titre de séjour' or residency permit.
Your wife can go to the local CPAM office upon arrival and fill out the CNAMTS 736 with her old social security number (if she has one). You will be covered as her dependent under the French public health insurance system PUMa. This will take a couple months, but you'll be able to cancel your private insurance (if the policy allows) once your wife receives her 'attestation de droits' which shows you as a dependent.
We wrote a blog on this topic a while back https://www.renestance.com/blog/french-health-insurance-for-everyone/ and you can also contact me directly if you have more questions.