Were there any formal diplomatic ties between Scotland/Moray under King Macbeth in the 1040s and the royal court of France(Henri II??) ? Would the court of King Macbeth have had Old Frankish speakers? Was Old Frankish a diplomatic language between Scotland/Moray/northern Scotland and France at that stage? I couldn’t find any specifics on ties between the two courts but I presume some trade would have existed between Moray and France
Latin was the international language of western Europe at that time. Diplomacy and non-local trade would all be in Latin.
Old Frankish appears to have evolved into other languages by the 11th century, so highly doubtful it was used with the Scots.
The Auld Alliance dates to 1295, so two centuries after Macbeth’s time.
Henry I. Henry II came a long, long time later.
There is a serious shortage of contemporary sources for 11th century Scotland. What we do know is that he made a pilgrimage to Rome in 1050. It is unlikely that a figure of his stature wouldn’t have had contact with Henry I during his trip (which took most of a year, back and forth and would have pretty likely crossed France twice since it was the easiest route). I think regular formal diplomatic contact is plausible, but not at all certain - royal administrations were overall not yet very large. But at least occasional formal diplomatic contact is reasonably likely. Regular semi-informal contacts via prominent merchants and pilgrims/traveling clerics might have been rather more likely.
1040 is well before the rise of the modern international law of diplomacy or even of nation states in today’s sense. There may well have been emissaries sent by one court to the other, but whether this counts as formal diplomatic relations is a fuzzy matter.
As it happens, I am currently sporadically working my way through a survey of Scottish history (albeit, one that’s about fifteen years out of date), and right now am on the chapter covering the early medieval kingdom. I’ll have to check when I get home, but I don’t recall any especial mention of France. During Macbeth’s reign, his primary foreign relations focus was on the English kingdoms to his south, and the aggressive, expansionist Norse kingdoms in Dublin, York, and - especially when he was mormaer of Moray - the Orkney Islands.