With respect to birth rate among immigrants, upon their arrival, they often have a higher fertility rate than other Canadians. But over time as they settle in, a balance is created and the significant gap between immigrant populations and others no longer exists.
To answer your question, when we look at census figures on language use among immigrants, it is clear that the source countries for immigration have had an effect.
For instance, when you compare the geographical origins of immigrants settling outside Quebec with those of immigrants settling in Quebec, you see two completely different pictures. Of course, there are still many immigrants from China and Asia in Quebec, but it is not comparable to the situation in Toronto, for instance and Vancouver.
In Quebec, we have noted that many immigrants comes from the Middle East, North Africa, Haiti and France. They already have a tendency to use French before they arrive in the country. Because of Quebec language laws, children are sent to French schools, so, there is already a process underway with respect to the use of the French-language at home and the public space. So, clearly the geographical origin of immigrants does have an effect on the ease with which they turn to French or not.
There has been an attempt in some minority communities outside Quebec to have francophone African immigrants settle there, who only spoke French. Obviously, that does improve their ability to integrate into the society but, on the other hand, if they don't know English, they are limited, for the reasons we all know.