I read he was sympathetic to the Lancastrians in particular, though he only ever reallly wanted an alliance with England, so was obviously support them. I say he wasn’t fully committed until after the Readeption because his chronicler described him as being very unhappy at Edward’s arrival in Burgundy, and thought the treaty that he had signed with Edward still applied despite the King changing. But it was certainly around that time he committed himself to the Yorkists.
I mean if he’s in Lorraine, it’s not going to be easy to get him, unless Charles has better luck at the Battle of Nancy. Alternatively he could end all support, and the Lancastrians and make them 15th century Jacobites.
Scotland would likely ally with France because of the Auld Alliance. Also there’s a chance Edward of Westminster might be the Duke of Lorraine here, since I have seen it suggested in other threads.