I talked a little about this in another pronunciation thread, saying:
Also, in lesson #43 [Dogen] says じ is pronounced as dʑ at the beginning of a word, and can often become ʑ after a vowel. (He also has more information on this in the video.) I believe he said じ and ぢ once had differences in pronunciation but in modern Japanese do not.
(I believe the “English J” you’re talking about is dʑ, and the “French J” is ʑ.)
Note that after ん or っ (small つ), it will have the dʑ pronunciation.
This pronunciation also applies to じゃ, じゅ and じょ.
This information came from Dogen’s phonetics series on Patreon, I’d highly recommend checking it out if you’d like to learn more about Japanese pronunciation and pitch accent.