When I look at how some song titles are sorted on Wikipedia (just one source), it seems that it can be similar to English: the “déterminant article” of French are ignored when sorted, and mentioned in parentheses after the rest of the title. Those include:

Le, la, les, l'

Un, une, des

This helps dispatching the title between many first letters, because otherwise a large number of titles will start with L or U. However, this is not the case of all lists that I’ve found, so keeping the title intact is also good.

For the capitalization, you will usually only capitalize the first word (except for “noms propres” that are always capitalized anyway.)