Start with the list of the busiest airports in France, including territories and overseas departments. It's likely that this omits particularly far-flung destinations, and if you really want to be thorough, you could manually audit the list against every airport in France (clicking into the sub-lists for territories) for those with regular commercial service. This is left as an exercise for the reader. But unless you happen to already be nearby, a small island airport with less than 20,000 passengers/year is not going to be the cheapest flight option anyway.
Use your browser to vertically select the list of IATA codes for all 77 airports (if your browser doesn't do this, Firefox does). Copy.
Use the text processing tool of your choice to turn that into a comma separated list.
Enjoy this list of airport codes:
Pop over to ITA Matrix and construct your search, using your preferred origin, dates, and other preferences, and pasting in the list of airports in the destination field:
Sort by price and enjoy the results:
You can also use the "see calendar of lowest fares" option if you don't have a particular date in mind, though it will take a while.