Coq means rooster in French and is not used as an insult or an euphemism for the penis at all. It's also what's on the logo.
Interestingly, coq is from Latin coccus (rooster) and cock is from Germanic kukkaz (rooster). I don't think there are many words that exist in both French and English with nearly identical pronunciation, the same meaning but unrelated roots!
The name should just change.