How can I convince my parents to let me fly alone?

As a parent, I would say that convincing them to let you travel outside of the country alone will be nearly impossible.

Nearly.

First, I would suggest that you engage in conversation about it in a polite and respectful manner, not having an attitude or being argumentative. Whining will not change their minds.

Look up the details - the unaccompanied minors service on airplanes. This costs a little extra, but someone with the airline will escort you from the gate to your seat on the plane, when you land and have to switch planes they will make sure you get to the next one, etc. Your parents can likely get gate passes to escort you to your first gate, and your aunt can be there at your final destination to pick you up.

Looking up the details of this will show maturity and responsibility, so do not just quote it. Actually look it up, print it out, highlight the applicable details and present it to them.

You might also make a packing list, and show that it does not include just your phone and charger but also clean underwear and toothpaste, etc. Again, it shows maturity and responsibility.

Write a letter in the form of an essay of what the trip would mean to you. Visiting family, seeing some sites in France, etc. Include ways it would be good for you in relation to your education (history, current events, language) and culturally (broadening your experiences, for instance).

Best wishes!

Offer to pay

I think you might be too young for a lengthy European trip like that.