Address search via the French Government.
French Address Search API is a free Open Data API that requires no API key, is served over HTTPS and has unconfirmed CORS support.

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Yes. The French Address Search API is listed in the Open Data category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
No. The French Address Search API requires no authentication, so you can start making requests without signing up.
CORS support for the French Address Search API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The French Address Search API is served over HTTPS, so it's safe to use in production.