Starting a PhD in Europe around March? I'm going to graduate with a physics degree at the end of next year (around December). I want to do my PhD in Europe, but I know that the academic year starts in September, and I don't think I can finish before that. 

Is it uncommon to begin work at the start of the year (February, March) rather than the usual date? Does that lower my chances of getting in to most universities? I mean, I'd have to tell them that I won't be able to go until the next year, and that seems pretty unorthodox. Maybe there's some people that won't have a problem with that, but I imagine they'll be in the minority. I'd probably lose the spot to someone that can start in August/September, wouldn't I?

What should I do? I don't think taking 6 months off is a good idea, and I definitely won't have any more courses or finals by that time.
The answer to your question really depends on which country in Europe you want to go. In Italy all the open PhD positions are assigned in the fall, while in the Netherlands every professor that has own grant can create a PhD position and hire you any time of the year. I guess this reflect also the different status that a PhD student has in these two countries: in Italy you are a student with a scholarship, in the Netherlands you are an employee of the university with a temporary contract.