I have translated "piglet" into French. I have found three translations: "porcelet m, petit cochon m, cochonnet m".
From Larousse:
porcelet = "Jeune porc ; goret."
petit cochon = {no entry}
cochonnet = "Boule plus petite que les autres, et qui sert de but dans le jeu de boules (synonyme but) ; le jeu de boules lui-même."
What is the difference between them?
Your definition of cochonnet from Larousse is right. According to le dictionnaire historique de la langue française, it is said :
En ancien français, cochon a produit cochonnet n. m. (XIIIe siècle) dont le sens de "cochon de lait" a été repris par porcelet, et qui garde des sens analogiques réalisant l'idée d'une petite boule ronde, désignant couramment une petite boule servant de but au jeu de boules (1542).
Porcelet, goret are correct translations for "piglet". You can use cochonnet as well, but it is an old french word and it will be understood as the "Jack" from the Pétanque game.
Petit cochon means "a pig of small size", it can also mean "a baby pig" in spoken language. According to me (native speaker), I would use Porcelet and petit cochon depending on the tone.
"Porcelet" means a pig in its young age.
"Petit cochon" may be translated by "little pig" (petit in terms of size) or "young pig" (petit in terms of age).
"Cochonnet" is a very specific term used to talk about the small ball acting as goal in the game of pétanque.
