Will I be at the same level as the other Anglophones?

If you have a good ear, you will probably lose the French accent, but don't forget that the British accents are very different from the Canadian. Also keep in mind that Anglophones do not only have the school input, but also the home input. Therefore your English vocabulary will probably never be quite up to that of people who learned it at home as children, from their parents and grandparents. Also, some cultural differences will remain. But if you are a dedicated student, you can function well in an English-speaking society.