Advice for emailing small, regional PE firms for unpaid internships

I'm an incoming freshman to a fairly unknown university in New England and I want to secure an unpaid internship for a local PE firm, however, due to the fact that I live in a reasonably rural area, these firms are sort of peppered around the region, so if I want to get an internship, I need to do a damn good job emailing the firm. I do not have any previous professional experience in finance, however, I do have marketable skills and knowledge that might give me a fighting chance. I am good with excel and I am in the middle of making my first DCF model (turned gridlines off, therefore I am a professional already), I am good with technical vocabulary, concepts, and financial theory, as when I am not at my day job, I really do enjoy analyzing publicly traded businesses and studying the associated vocab and concepts.

So, how should I approach the firm? I would assume they wouldn't be super pleased if I just said "I'm an incoming freshman who likes finance and I want to work for free for 3 months, here's my resume with no relevant experience." What's the right way? A long explanation of how I can help the firm? A chat over the phone with the CFO?

Thank you.