Well, you English had poached our court in 1603, and all the Scottish lute manuscripts come from after that, so the Scottish court did not exist, and therefore couldn't be influenced by French lutenists.
The 11c lute, though, was definitely a French invention, and there are 252 pieces in Balcarres for it, with about 50 of them being of French origin. My favourite is Belle Hereuse (track 34).
In the absence of a Court, the tunes were notated by landed amateurs, but also a new class of professional musicians, including one John Beck, who features throughout Balcarres. Mathew Spring desperately tried make a German connection with the name Beck, but it is a Lowland Scots version of the Gaelic, Beag - pronounced the same as Beck - meaning small. So, John Small or John Little would be an English translation.
We in Scotland must thank Beck for winning an important court case. He challenged the Parliament's (that's the Scottish Parliament, which wasn't disbanded until 1707) sole right to promote concerts. He won the case, and since then we have been able to put on concerts without first having to apply to the parliament.
Although the estate of Balcarres is in Fife, Beck was active in Edinburgh, where he might well have met French musicians. The music shows an interest in developing a bass line, which Scottish lute manuscripts had not shown any interest in before.
I don't know if I'll ever finish recording all 252 pieces - I'm two fifths of the way through it. Maybe if I live another twenty years, and can still hold a lute...