Upvote:1
Since both countries / policies are independent. There shouldn't be any problem.
To apply for an F-1 you should have been accepted to an US school. Same goes for the Canadian student permit. So, I find it strange that you want to get accepted to schools in two different countries and that you want to apply for visas to attend both, but technically, that shouldn't be an issue.
Keep in mind that both permits expire soon after your education program is done or you are no longer enrolled.