Guten Morgen in Deutschland. Our bullfrogs are not native to North America, but are transplants from Africa that have spread across the continent. Maybe they are present in parts of Europe, too. What kind of frogs do they eat in France?
As to bowhunting here in the USA, each state has its own rules. In most cases you must have a hunter safety card to get a license if under age 16 or 18 (varies). In many states you can hunt unprotected non-game species with no license. Let us know where in the U.S. you want to hunt, and we can direct you to the right set of game regulations.
Oddly, here in Oregon we have strict seasons and bag limits for gray squirrels, but no rules at all on hunting rabbits.