Both countries, for fairly obvious reasons, were generally at odds with England, and therefore were natural allies for each other.
The French King even used to be protected by the “Scottish Guard” a 100 man force of Scots. I have no idea how that came about either.
Monarchs throughout history have always had the problem that guards drawn from among their own people reflect those people's political divisions, and tend to determine who the monarch will be, if necessary by offing the current one. Or they might be unwilling to kill their own people in time of revolt.
See Praetorian Guard, Russian Guards, Janissary Corps, etc.
To avoid this, monarchs often brought in foreigners to act as their primary guards. Caligula used Germans. Byzantine emperors used Varangians. Most Muslim sultans had Turkish or Nubian slave guards. The French kings had Swiss and Scottish guards. The popes still do.
The locals hate the foreign guards, who return the feeling, and are perfectly willing to slaughter them when required.
So, are all the Secret Service around the Obama family black? Does anyone know for sure?