Oh oui!! I miss those Averty radio shows.
He was some kind of a Phil Schaap on speed! A fast talker indeed and very exacting on details - any detail - on the recordings he played, indicating the master number (including going as far as detailing the take number)!
Great memories of some of those shows...
afaic Kenny Dorham was the quintessential BN trumpet player of the 60s, as much as Miles and Clifford Brown were in the 50s.
Concise, always up to the point, he is the player from that decade I enjoy more than ever!
You can try these...
http://www.tsfjazz.com/accueil.php
http://www.streamingthe.net/Jazz-Radio-Swing-101.2-FM-Limoges/p/11372
not really sure you'll improve your french but they have jazz all day long!