How do I deal with Gavelkind inheritance?

Problem: once you die, your sons will split up your lands. Since you have more than one top-level title (duchy, in this case), your multiple sons will split into multiple independent realms.

Solution 1: MURDER. You have too many sons. Make terrible things happen to all but one of your sons. Cross your fingers and hope your sole surviving son doesn't die until after you do. ("Terrible things" include assassination, putting them at the head of a far-too-small army and sending them to war, making them the court chaplain and sending them to proselytize to the pagans, and rarely-available plots to kill.)

Solution 2: TREASON. If you only have one top-level title, then your oldest son gets that title, and your other sons will end up as vassals to your oldest son. It's time to become King of France. You'll need either a majority of the counties in France, or a claim on the French crown, or permission from the Pope to invade France (which will probably involve excommunicating the French king first). But before you can take that final step to acquire the French throne, you'll need to be independent from France itself; this can be made much easier if several other dukes are attempting to declare independence at the same time. (Try joining or starting the Faction for Independence?)

Note that your lands will still be split up among your sons, but at least your eldest son will be your other sons' liege. Your eldest son probably won't have a full demesne after the inheritance kicks off, but maybe you can pick up some counties elsewhere, via holy wars or pressing claims.

Solution 3: WAR. Your sons will end up as independent nobles from each other (as vassals of the King of France), but they'll all have strong claims on each other. Your eldest son will end up with all your money and the best lands, so have him go to war to reclaim the rest of your former lands! Make sure he gets enough money to hire mercenaries, and it will be even easier.

Note that if your liege has Medium Crown Authority or higher, you won't be able to do this. At Medium authority, wars between vassals are prohibited.

Solution 4: ....Peaceful discussion? Once per generation, you may change your inheritance laws. If all of your immediate vassals have a positive opinion of you, and they aren't at war with each other, and you've ruled for at least 10 years, then just change your inheritance law to something else. Primogeniture requires High crown authority, but you should always be able to get Elective. (Elective has its own troubles, but you should be okay for at least this one generation.) Primogeniture is the easiest succession law to control, but your pretenders will dislike you (a net -50 opinion penalty!), and you'll lose the +5 opinion bonus you had with your other vassals, but it's (usually) better than splitting up your lands. Also, switching out of gavelkind will reduce your demesne size a bit.

For more details, wander through the succession and gavelkind sections of the CK2 wiki.

There is another way to handle having multiple sons with gavelkind, make your younger sons bishops (either build churchs in lands you control, revoke the bishop title from someone, or conquer a county in a holy war which has a bishop/mosque in it). This will disqualify them from succession. If at any point your heir dies you can revoke this bishop title and they will become the new heir to the entire realm.