Mathilde and Julien exist on fairly decent terms as friends, since they both seem to feel secure about their love for one another. Now it's more a matter of sitting on it and seeing where it goes with time.
But here comes the plot bomb: Mathilde realizes that she's pregnant. Yup.
She uses this fact as leverage to finally make Julien believe that they'll be together forever. She says she's going to tell her father immediately and she's going to leave the house to marry Julien, even if she does it in disgrace.
Mathilde writes a letter to her father announcing her pregnancy and saying that she's going to marry Julien.
She'd prefer it if her father could provide Julien with some money to start their new life together, but she understands if he (the marquis) is too angry.
Not long after, the marquis summons Julien for a little chat.