Do a search for Boat Insurance on this forum and you will find most of the answers to your questions. But, basically -
1. If your boat still has an outstanding bank loan, you will have to carry insurance. If you go offshore
- leave USA waters, you will need to get "offshore" insurance as most "in home country" home/auto insurers who also cover your boat will not cover it outside of your territorial waters.
2. If you do not have an outstanding loan on the boat but have a large amount invested in the boat and want to get some of that money
back if the boat is lost/damaged then you will have insurance either "domestic" or "offshore" as appropriate to your cruising destinations.
3. If you don't mind losing your investment in the boat should you have a lose/damage the boat then you can get by with "liability-only" boat insurance which covers the requirements of marinas
4. If you don't ever intend to stay in a modern marina or upscale boatyard that is outside the home country's waters, then you can go "naked" or "self-insured" which means - no insurance.
5. Very few countries require you to prove insurance to enter their country - Mexico is one of them and I suspect their requirement has more to do with bringing in money
for their country's insurance companies than worrying about your boat.
6. Once you have an "offshore cruising" insurance policy (full or liability-only) on the boat you can satisfy most all the countries of the world without having "local" coverage.
7. Consult Noonsite.com for specifics about any particular country you are intending to visit.
8. The French Visa insurance requirement has to do with formal Visa's rather than "instant tourist" visas. And the French are primarily concerned with your being covered to send yourself back to your home country with what is called "repatriation" insurance. You can get "International Medical" insurance including repatriation from a number of sources. Search for that subject on CF and you will find all your questions answered.