I'd note also that France isn't the most navally oriented of nations, in Civ 5 or historically. Try England out for a warmonger naval game, and marvel at the Ship of the Line blasting chunks out of enemy cities. Then for a totally different feel, try Denmark and play at viking raiding. Ignore the info here saying Denmark is the worst civ, as civ tiering isn't really important at anything less than Emperor difficulty: everyone is worth a try. Then switch to Venice for a totally different game again, and build a merchant empire that sends masses of food cargo ships back to Venice, and marvel at the medieval megalopolis that results.
The key promotion for your frigates/ships of the line is +1 Range. To get there, build Galleass early, hunt barbarians and if you want, find a city state that you're happy to XP farm. Personally I hold off the full naval war till I'm at frigates.
Frigates with +1 range are amazing, as you can hang out of city attack range, and bombard them to nothing, then take the city with a naval melee unit of the lowest quality.
Number one problem with Frigates: they need Iron. Make sure you reveal iron on the map early, and build a city near iron. (on is faster for instant iron, but near is better, as you only need the iron when you hit frigates, and mined iron has a high hammers output). It sometimes happens that you can't found a city near iron. In this case, don't be afraid to invest in a big bribe to get a city state with iron as your ally. Its that important. Vitally, don't waste iron on anything but frigates.
So basically, get your naval techs, found some colonies to get iron should you need to do so, use cargoships to transport food bonuses about, get three or four galleasses, get them XPed up, then upgrade them to Frigates.
Then, essentially, take them to war. Three to four frigates plus a single melee ship will drop a city in 1 to 3 turns, depending on how quickly you set up. Before the naval tech has moved to the next level, you should have won a domination victory.