I have a Regina Sport, and here's what I found on the net so far.
Regina Sport is a French brand, owned by the Ets Betbeder in Oloron-Ste-Marie. The frames were reportedly made by Cycles CAYRE, a small local artisan. Besides 'Regina Sport', they were also badged 'Lapebie' and 'Louison Bobet'
Here's mine. As bought. Reynolds 531 frame and fork:
Zeus fork crown:
