The obvious connection between the Longbottoms and the Blacks is that B. Lastrange (sp?) tortured Neville's parents and she is a Black.

However, Regulus had turned away from the dark arts and Voldemort so any old connection would have been broken and new ones may have been made.

Anyway - Regulus was just one guess and probably not a good one. It is unlikely that Regulus would have survived drinking the poison in the cave when he stole the horcrux locket (unless someone else was there to drink the poison).