I did end up having a café with my directrice on Sunday, and it was great! We talked a lot about school and differences between France and the US, some personal info, etc. No awkward pauses either! The conversation just kept rolling. I hope she feels more comfortable with me now and will maybe eventually invite me to meet her friends? Or at least hang out with her more often? Fingers crossed!
So this time being proactive and not a coward produced good results. Maybe now I should start working on the remplaçant at Directeur Napoleon Complex School (L School). She doesn't talk much and seems kind of shy. She's probably like me (or like I was), a little unsure of her place in the school since she's only there once a week, and the people who work at the school are kind of cliquey and catty so I'm sure she doesn't have much desire to talk much either (I know I don't). I think we can bond over the fact that we're normal people at a school full of crazies. As long as she is normal, because I can't really vouch for that fact yet. I'll have to make more of an effort to speak to her at recess to see if there's a possibility.