Not legal courts. By the late middle ages, I already see quite a few "French" texts appearing in places outside of France (not just the language of the Ile de France itself, but also closely related languages like Provençal, Norman French and so on... Much later, with Versailles, French somehow reasserted itself again but, why?
Is the original influence and expansion of the languages spoken in modern day France perhaps due to the comparitively massive population France had throughout the middle ages or?
One thing comes to my mind for the late middle ages - but it concerns mostly "French" lifestyle at courts.
The Duchy of Burgundy was one of the wealthiest and powerful territories of the 15th century (The classic on the topic would be: Johan Huizinga: The Autumn of the Middle Ages 1919). They spoke of course french, since the four dukes Phillipe l'Hardi (the bold), Jean sans Peur (the fearless), Philippe le Bon (the good), Charles le temeraire (the bold) came from a sideline of the Valois kings. When Charles died his territory included Burgundy, modern Belgium, Netherlands, Luxembourg, Lorraine (the 'bold' in his name is a negative one, he quite foolishly had himself killed by the Swiss).
While France and England killed each other in the 100-years war the Burgundy dukes played a dangerous game, profiting immensely (for a price, Jean Sans Peur got himself killed by the French Dauphin). They were also the ones who delivered Jean d'Arc to the English. Charles eventually was a serious contender for the Imperial crown due to his possessions in the Empire.
But he died without a son, had a daughter however, Mary of Burgundy - she was unmarried and certainly the best match in Europe simply for her wealth and territories. She eventually married Maximilian of Habsburg - who would become Emperor Maximilian I. While her forebear's territory broke apart, some of it fell to the Habsburg family - who took over the elegant court ceremonies of Burgundy - including the noble Order of the Golden Fleece. They spread it in their lands: so in Austria and Spain (later it became commonly known as Spanish Court Ceremony) and from there throughout Europe.
I'm honestly not entirely sure that this included the French language, but since it was the center of chivalry I consider it quite realistic.