How about a France England football cup between teams in ligue 2 and the championship of England. It would be a fun trophy. I think Scottish sides should play Danish or Norwegian sides in a similar trophy.
Ligue 2 is the second division of French football. It is one of two divisions making up the LFP, the other being Ligue 1, which is France's top division. The 20 clubs that make up Ligue 2 play each other twice during the season, creating a 38-match schedule. At the end of the season, the top three clubs are promoted to Ligue 1 for the following season, while the bottom three clubs of Ligue 1 are relegated to Ligue 2. The bottom three teams of Ligue 2 are relegated to Championnat National.
The France - English cup
Have a preliminary round to get to 16 teams from each nation. That creating 32 sides. Then have a knockout trophy from the remaining teams. The final played in Wembley and Stade De France interchangeably.