Two years certainly could be enough, but it really depends what the environment. If OP, like many English speakers who live in France for a couple of years, was teaching English, or studying in an English speaking postgraduate course, and then socialising with a mix of people from different places, who all use English as their shared language... It can be pretty easy to miss out on a lot of immersion.
And the level of language to comfortably phone up a hospital, explain a slightly odd request and be bounced around different departments with the administration... I know plenty of native French speakers who would avoid doing that.