Having lived in France since June 2009, I can tell you that it is possible to learn French without spending a single Euro. I studied 20 hours a week, and after five months I was fluent enough to get my first job as a waitress.
When I arrived in the southern French town of Millau, I barely knew basics like bonjour and merci. Though I watched TV and listened to the radio to get used to the sound of the language, I realized I needed something more. I asked at the local library about French courses for foreigners and was told about the Myriade Association that offers courses to all levels of language learners.