The men beat hosts France in the final in Colomiers and their female counterparts overcame home team Russia in Kazan earlier in the day in two qualifying competitions for European nations.
England represented Team GB in Olympic qualifying for the event as they did four years ago in reaching rugby sevens' first appearance at the Games.
Japan have automatically qualified for both competitions for their home Olympics.
Reigning champions Fiji, the US, New Zealand, South Africa, Argentina and Canada have already guaranteed their spots among the 12 teams for the men's events.
Rio winners Australia, New Zealand, the US, Canada, and Brazil have qualified for the women's tournament.
The winners from qualifying competitions in Oceania, Africa and Asia will also feature in Japan.
The two runners-up from all the tournaments will play two 12-team competitions for both men's and women's sides next June for the final places in Tokyo.