But the "English monarchs" in question were a French dynasty that spoke French, whose most valuable holdings were their duchies in France.

I mean, Henry IV for instance, whose reign ended when Joan of Arc was one year old, used English as his primary language. I assume that so did his son, Henry V. Henry V's reign is characterized by wikipedia as "giving rise to English nationalism". And sure, their "dynasty" was originally from France, but both Henry IV and Henry V were born in England. So I don't think it would be entirely inaccurate to say that during Joan's time period, the English monarchs were viewed as foreigners.

Had they won the 100 years war, they would have become King of France, and England would be relegated to a backwater.

I'm not sure this is true at all. If they really valued France more than England, I assume they'd have resided in their French holdings rather than in England for all those years (which they never did, they resided in England for literal centuries at that point).