It is not mandatory on paper, but you are going to have a really hard time convincing the Interviewer (for CSQ) that you still intend to live in QC even without any french. The only way they could accept it is that you otherwise qualify and just haven't caught up to speed with the language for the time being. So you still would be expected to speak SOME french in interview.
Not to mention the insanely long and unpredictable time frame (could take 7 months to 2+ years for CSQ only, then add a year or more for the PR application itself). So you are potentially looking at a process that might take 3 years in receiving PR. The only reliable exception to this is with advanced intermediate french you get CSQ much sooner. E.g. for a highly skilled person with job, you get it in a couple weeks.