I should have put it in an answer: Not a native French speaker, but I'd probably try: Juste pour le fun. Or maybe: Juste pour aucune raison. Right out of my Le Grand Robert: "Amusement, plaisir. C'est le fun ! C'est juste pour le fun."

Hello, Well, I did some research, because I was not very sure. "Just for the of it" has several meanings. Indeed, there is "Juste pour rire", but it means also "pour rien", "comme ça", "pour le plaisir". This expression means in broad terms that you're doing something for no reason at all.

Not a native French speaker, but I'd probably try: Juste pour le fun. Or maybe: Juste pour aucune raison. Right out of my Le Grand Robert: "Amusement, plaisir. C'est le fun ! C'est juste pour le fun."