You're quite right. The French didn't really want to get involved in the New World aside from staking a claim, and domestically they where very busy picking on their protestant citizens, so they thought lets send the protestants to the New World and kill two birds with one stone as it were.
One such "convoy" was lead by Jean Ribault to the French Fort Caroline where he was to be the new governor. On arrival he suggested attacking the Spainish at nearby Saint Augustine, or San Agustín, the out going governor advised against this - not least because they were coming into storm season and how the storms there weren't like European storms.
Ribault dismisses this and sets off to stuff the Spanish, finds it's not as easy as he thought, so sails into deeper waters to disengage and right into a storm. he and his small fleet are shipwrecked and the survivors washed ashore are spotted by native Indian. Being allied to Spain they go and tell the governor of St. Augustine one Pedro Menéndez de Avilés who then tears off down the coast, rounds up the survivors and kills them all bar the handful who can comnvince him they're Catholic.
Fascinating stuff.