Several suggestions for you.
Yes you can do an exchange and a co-op placement. However, be warned that this may stretch out your degree by a few months to a year. IMO, there are worse things than taking an extra year at school, especially when you'll have great work experience from your co op and great cultural experiences from your exchange.
Secondly, yes you can do an exchange to France even if you don't speak much French. Complete immersion is the best way to learn a language! I did an internship in France last year and spoke barely any French at the start... it's hard at first but if you want to learn and put in the effort, you will. You'll learn faster than any class you'll ever take, and you'll learn how people actually
speak rather than formalities which people may or may not use in real life.
If you don't want to take a French class at university, I highly recommend this program: http://www.myexplore.ca/en/page/?program_description
Its a five week intensive French-immersion program, at various locations in Quebec and it's free if you get a bursary (which is likely if you're a first time applicant). I know it's a stretch to take 5 weeks off in a summer, especially if you need to work and stuff but it's SO worth it. I did it this past summer and loved it.
From this program, my internship in France, and some self-study to keep up, I'm pretty comfortable in French now and I haven't taken a French class since grade 10. Definitely do-able