Chelsea thumped PSG 3-0, with the European champions having Joao Neves sent off late on. Cole Palmer struck twice, with Joao Pedro also scoring on the day.
James said after lifting the trophy: “It's amazing for me. Since a little boy I supported this team. I just wanted to play for this club just once. That would have been enough for me. To captain the team and lead them to two trophies this season has been a dream for me.
“I think for sure we are moving in the right direction. Winning this trophy against such good opposition sends a big statement.
“I'm happy with how much the club has progressed. I hope next season we're competing in the Premier League to win the title and competing to go far in the Champions League as well.
"We beat the champions of Europe. They beat, as people told me, all the other English teams. So I know for sure it gives us confidence moving forward. I think we'll take this moving forward as well.”