That's the OTL "Ancien Régime" COA of the late 18th century. It wasn't used during the Restoration Era despite going back to a monarchical Kingdom following the 1st Republic, Directorate, Consulate and Napoleonic Imperial era.That's the OTL French Coat of Arms.
The Reason I mention this is that it would seem to imply either that the Capetian monarchy continued without interruption or that it was readopted during the Restoration, restoring to the kingdom of Navarre some form of autonomy within the Kingdom of France (up until 1792, it had a separate legal system and gave equal rights to Huguenots) and that the monarchy continued from then on. It might be a good idea to determine which is true if only from a narrative point of view.
Also, from a design point of view, I would advise having the 4 Fleur-de-Lys in the quarters at a 45 degree angle pointing either inward or outward.