Bonjour, je m'appelle Paul.
Here's why:
* Bonjour: This is the standard greeting in French.
* je m'appelle: This literally translates to "I call myself," but it's the standard phrase for "my name is" in French.
* Paul: The name stays the same.
You could also use "Salut" as a more informal greeting, but "Bonjour" is generally more polite.