Of course, everything depends on the geographic reference you use. At the provincial level, results may be different from those you'll get if you use a more regional scale. For example, in Saint-Boniface, Manitoba, a major effort has been made to welcome and integrate French-language immigrants. At the local level, they have achieved quite significant success.
However, survey results have shown that immigrants who settle in minority francophone areas are disadvantaged in the labour market if they do not know English because that happens. Consequently, there is nevertheless a fairly significant need to know both official languages in order to integrate, economically speaking.
I wouldn't say that immigration raises or lowers the assimilation rate. You clearly can't ask immigrants to do what francophones can't do themselves. Having said that, we have to pay attention to the way we define the issue of assimilation because we realize that a significant proportion of francophones speak English at home. On the other hand, French is regularly used in the home, which, in a way, may allow French to be used in the community.
The issue of assimilation is not necessarily clear. It doesn't just happen in the family environment; it also comes into play in the community. If there are community centres and centres providing services in the language, it will be possible to increase the importance and use of French.