The GB Lions lost in the quarter-finals to Russia but the GB Royals overcame France 33-17 in the final.
Tries from Ollie Lindsay-Hague (2), Alex Davis, James Rodwell and Ruaridh McConnochie gave GB Royals victory.
GB head coach Simon Amor is due to name his final squad for Rio on 19 July.
Great Britain continued their Olympic preparations as one of the two teams the squad fielded secured victory in the Rugby Europe Sevens Grand Prix Series event in Exeter.