The common language is the ultimate objective. In the rest of Canada, English is the common language. In places other than Quebec, when people who speak different languages want to talk to each other, they speak English.
The objective for Quebec is for French to be the language that brings people of all origins together, regardless of their first language, so they can have a shared public space and so we can have a cohesive society.
I do not see the problem with the term “common language”. That said, I do not wish to drag out the debate needlessly.