According to the following excerpt from Notes sur l'Artillerie dictées par Napoleon à St. Helene au Baron Gourgaud (1875 excerpt from Revue d'Artillerie), Napoleon was inspired by the capture of Shrapnel ammunition at the Battle of Albuera to order General Eblé to study these weapons (possibly with a view to replicating them):
"NOTE C.
Sur le sens à attribuer au mot: Grenade.
Par ce nom, Napoléon a sans doute voulu désigner les obus pleins de balles de plomb inventés par Shrapnel et essayés en Angleterre dès 1803.
Un obusier anglais et deux caissons remplis de ces projectiles ayant été pris à la bataille d'Albuera (16 mai 1811), l'Empereur avait fait ordonner (lettre du 22 août 1811) au général Eblé, président intérimaire du Comité, de faire entreprendre des expériences
pour déterminer le mode de chargement de ces obus à balles; il attachait dès lors une grande importance à leur propriété d'éclater au bout de leur course et de porter au loin la
mitraille."
I have looked without success for the August 22, 1811 letter to Eblé in Napoleon's official correspondence and several other compilations of his letter and decisions. I would consequently appreciate assistance in locating a copy of this letter.
The French experiments to develop spherical case shot apparently occurred during 1806. It is mentioned briefly in John Elting's Swords Around a Throne on page 487 and 488.
Apparently, the French actually carried out experiments with their 'version' of the round but it was only produced in a limited experiment and was not put into full production.
The French experimented with rockets in 1810 and both Eble and Lariboissiere were involved with it. Their rockets were not as good as Congreve's but the Dane's, probably based on their actual experience on the receiving end of British rocket fire in Copenhagen, and they actually developed reliable fragmentation, explosive, and incindiary rockets and when occupying and besieged in Hamburg, began his own rocket program which was later ignored by the restored Bourbons.
Other innovations, these prompted by Napoleon, was the attempt to develop an 8-inch naval gun that could successfully fire explosive shells. He also wanted the light naval guns on smaller warships replaced on heavier pieces designed as pivot guns.
In 1807 Andreossy conducted tests using shell fire against ships' hulls, which was what prompted Napoleon to order his Minister de la Marine, Denis Decres, to develop the 8-inch shell-firing naval gun.
It might be worth asking whether it ever existed. There is plenty of rewriting of history in the Memoires. I have also seen a kind of reverse position concerning a letter supposedly written by N at the end of 96 to Dumas, thanking him for providing key intelligence. However, it is the invention of his son, Alexandre, the famous novelist.