Dear [insert name of potential boss here],
After reading your ad on [insert name of job forum here], I would like to submit my resume for your consideration, even though I'm not sure it will help my cause: it will tell you that I'm an English-French translator, hence that I should be able to write - who knows, though... -, but it won't really mention my passion for all things cinema, American or otherwise. Similarly, it won't mention that I'm a contributor on a collective blog about Paris, for a Britain-based readership (Voice of a City Paris*, if you want some writing samples). And of course, there is the conspicuous absence of any experience in production.
Having no precise idea of what this internship covers, it's difficult for me to say that I'm the best candidate for the job, but hey, it's worth a try: I'm the best candidate for the job, and I really hope that you will consider my application.
So... you think it would fly?
*Notice the clever plug...