For emphasis, meaning "only me":
* Moi seul(e) (male/female) - This emphasizes that it's only you.
* Seulement moi - This is a more literal translation of "just me" and emphasizes the exclusivity.
To express that you're doing something alone:
* Moi tout seul(e) (male/female) - This implies you're doing something on your own.
* Tout(e) seul(e) (male/female) - This emphasizes the solitude.
In a casual context:
* Just moi - This is a more informal way to say "just me."
The best way to say "just me" in French will depend on the specific situation and the level of formality you want to convey.