If the Girl King is indeed inspired from the play "Christine, la reine garçon" as the article I read mentioned, I'm not sure François has a big role in it. Christine was a feminist, torn between her love for women and her royal duties. It's a great character, a very active role for the actress.
Christine's cousin (Charles/Karl aka François) was in love with her and from her wikipedia we learn that:
He was infatuated with her and they became secretly engaged before he left in 1642 to serve in the army in Germany for three years.
He reappeared few years later when she abdicated her throne on 5 June 1654 in favor of him. Charles, who was crowned later on that day, proposed her again to marry. Christina laughed and left the country, hoping for a warm reception in Catholic countries. Charles had to move into an empty palace.
You probably all already talked about that and I'm late to the party, sorry if that's the case.
