While my family definitely has its origins in Scotland, there was a surname geneology database I was looking at in Greenwich a few years ago with respect to heraldry etc and it listed Northern France (with no mention of Scotland, so a rather incomplete database I guess) as a source of the name.
So the question is probably more a case of how far back you want to go... I would presume it's origins are Scottish or Irish until either pre-1700 when the Scots were the King of France's bodyguards and you have a possible mix / transfer of men between the two countries. Pre-1400, a possible 'relocation' of many French to Scotland, or 1066 era with the Norman invasion.
The latter is the most difficult to explain since you would expect a greater number with the name to stem from southern England, not Scotland, which is clearly not the case. This is of course assuming the database I looked at was accurate and it does have French origins.