Unfortunately, the king is surrounded by courtiers, whose job it is to make access difficult. Ponceludon can make progress only by participating in the aristocratic pastime of eloquent insults. If he is good at this, and he is, he will receive social invitations of increasing importance, leading to the king himself.
Ponceludon makes both friends and enemies. His most loyal ally is the Marquis de Bellegarde (Jean Rochefort), who just happens to have an unwed drop-dead gorgeous daughter, Mathilde (Judith Godreche). We suspect a romantic relationship will bloom between Ponceludon and the science-inclined Mathilde. We suspect correctly.
The other person willing to help Ponceludon is the Madame de Blayac (Fanny Ardant). Blayac is a clever socialite with an inside track to His Majesty. But Blayac will only help Ponceludon if he becomes her kept man, when naturally he prefers the younger and much hotter Mathilde.
How I felt about it. If my plot summary comes off as sarcastic, it is only reflecting the theme of the movie. Making fun of someone, particularly someone that Versailles society finds tiresome or an obstacle, is the key to popularity. It is like being in Junior High all over again, only the stakes are higher. The social outcasts, and their families, are removed from court favor, and any income that it may provide.
As expected of the film's hero, Ponceludon would normally be above all this, except that he wants a government handout to drain his swamps, and there is no other way to achieve this. As an outsider, his enemies and jealous rivals are many. They conspire against him, betray him, and challenge him to duels, until he finally become sufficiently annoyed to go home. Which is what his enemies wanted all along.
At least Ponceludon can console himself with spectacularly beautiful Mathilde. Her character could easily be written out, and exists in the first place only because producers know the importance of adding a hottie. And not just any hottie, but a smart, learned, courageous, and loyal one who performs interesting scientific experiments and just happens to have a relatively wealthy father. She can turn Ponceludon's failure into success, since the only thing he ultimately accomplishes in Versailles is winning her hand.