Could this also mean that someone is playing a game "with him" because it sounds like that if listening.
If you're hearing this that would be more likely, in fact that name isn't French (it would be Louis) and this one is from Spanish origin so French people would tell it with the Spanish pronunciation (so with the "s" pronounced and the "u" sound becoming "ou", something like "Louisse"). As ripcurlgirl said, the audio isn't always very good on Duolingo.
You're right. Je joue avec lui means "I play with him" and the two sound identical if you received this as an audio translation, though, in my experience on DL, they don't usually put amiguous sound files on. If they have, and you get it again, report it to the developers.
Forgive the unintended innuendo - wants wrong with "I play with hers" as per the dropdown hints