The IPA is your best friend!
Not sure if this has been posted or not. IPA is your best friend for learning the vowels . It also gives a standardized frame work for describing sounds and gives examples of words containing the sound in English and French. Google "French IPA" and it will bring up a chart in wiki.
You are absolutely right! In fact, it is a good idea to use the IPA to learn the sounds of any language. However, the terminology can be hard to understand unless one has knowledge of phonetics, so find an IPA chart that has sound files attached to each sound or some sort of audio tool to learn the pronunciation. It would be great if Duolingo could provide such IPA charts with sounds for the languages it offers.