According to historic accounts, Vatel's death happened because of a miscommunication. When asking the fish vendor "is this all?", Vatel wanted to know if the quantity given was the entire supply of fish for that day. However, the vendor understood that Vatel was referring only to his own stock. Ignoring that other vendors when coming, Vatel took his own life.
When the cooks discover that the cream has gone sour, Vatel whips it with some sugar and orders the servers to present it as "a new version of Chantilly cream". This is a nod to the real Francois Vatel being falsely credited as having invented Chantilly cream while serving as the maître d'hôtel of Château de Chantilly. Flavored, sweetened whipped cream had been around for about a hundred years prior, while the first ever record of the term "Chantilly Cream" itself did not occur until the mid 1700's, approximately one hundred years after the film's setting.
Much modern knowledge of the festivities comes from the letters of historical figure Madame de Sévigné, a popular aristocrat whose letters were copied for public circulation at the time, and who knew Vatel personally. She notes that the fireworks, obscured by the fog and bright moonlight, cost 16,000 francs, and the entertainment during which Vatel committed suicide cost 50,000 francs (roughly 1 million USD in modern currency).
Louis XIV tells the Prince of Condé of an incident about the King of Holland having commissioned a painting showing one of his ships in flames. The King is referring to a painting by Adriaen van Diest showing the destruction of his flagship the Soleil Royal at the Battle of La Hogue in 1692. The Soleil Royal was regarded the most powerful ship, having been named after Louis XIV himself, and its loss was a great embarrassment to the French navy. Actually, when the painting was described to him by an ambassador, Louis took it as a personal offense and influenced into a war.
Anne Montausier is not a historically-noted mistress or lover of King Louis XIV.