Formal:
* Je parle plusieurs langues. (Most common and straightforward)
* Je maîtrise plusieurs langues. (Emphasizes fluency)
Informal:
* Je parle plein de langues. (Literally "I speak a lot of languages")
* Je suis polyglotte. (More literal for "polyglot")
You could also use a phrase like:
* Je suis capable de parler plusieurs langues. (I am capable of speaking several languages)
The best option depends on the context and your desired level of formality.