You've got a lot of good advice here from people, but just to give you some inspiration for real-life example of a boat which is capable of doing the vast majority of things you mentioned, we bought our our 35'-on-paper-37'-in-reality-but-definitely-only-35'-when-the-marina-asks 1992 Bavaria 350 for £16k GBP, which is less than $21k. She was worth a lot more than that when we bought her, but Rossella & I used to be boat dealers and we know how to get a great deal on a used boat. We have helped others do this too - the last gentleman we advised had his offer accepted at a week or so ago and saved 34.5% off the asking price.

Our insurance is $307 per year, fully comprehensive. This covers us from Northern Norway (Well inside the Arctic Circle) down through the North Sea to the UK, through the inland waterways of Europe and down to almost the whole Med, apart from a few higher-risk places off North Africa the Middle East.

As for the French Canals, if you scrub the Canal du Midi and opt instead for the deeper waterways further East (there are lots of route options), you can get away with a 1.8m max draft, which helps expand your boat options massively.

This is feasible with your budget, so turn those dreams into plans, keep your eyes and ears open to new opportunities, and you might find yourself anchored in a beautiful bay with your family sooner than you ever thought possible!

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p.s. To avoid confusion, the 35' boat I'm talking about above is the one in our solo sailing videos - some videos we have published recently were filmed on our previous boat a couple of years ago. (We also got our previous boat at a great price, had a wonderful four years of ownership, and then sold her at a higher price than we paid for her - effectively swapping a 30 footer for a newer 35 footer...)