Finely chop the fennel bulb, onion, and about 4 or 5 cloves of garlic. In your largest saucepan (one with a good lid), add the olive oil, and cook over medium heat until slightly translucent. It's important to not burn anything here, so be mindful of the temperature—sweating this mixture should take about 10 min.
Turn the heat to high and add in the crème fraîche and wine. Give it a few good stirs, then add the mussels. Give everything a good mix, then quickly cover. After a couple of minutes, give it a good mix again. You'll be ready to serve about 3-4 min after you see the majority of them open. This is the most important part. Don't be looking for every single one to open, or you'll overcook, and they'll be chewy. Throw away any mussels that didn't open. That's it!