Michelin has a "classic" series of tires they still produce, one being the mid 1960's XAS series sold through Coker, which was an update from their earlier radial. They're relatively narrow tires with a rounded tread that's more slow speed steering "friendly" than modern flat tread radials on non power steering cars. They come blackwall only, and have an unusual tread design you might not like on your vintage car.
I ran them on my Aero in the early 70's and liked them enough to spring for a set on it's current restoration. I wouldn't be too concerned about needing modern "radial" rims, Michelin started making radials (I think) in 1949. As far as I know, they don't reproduce the 50's version superseded by the XAS series.