Thank you all for the advices, we kept that in mind when we brought her home last night. I'm more used to dogs than cats, so it'll take me a while to get used to the "cat" way of doing things!
Turns out, once they shaved her for the surgery, they saw she already had a scar, so they're 99% sure she was sterilized already! I was very happy she didn't have to go through surgery. A new environment is enough emotion for one day!
So we brought her home, we showed her the litter box and then we left her alone for a little while. But she was very curious, she was inspecting every corner of the house and found the food pretty quickly!
As some of you predicted she was avoiding us at first and hiding under the bed if we got too close, but just after an hour, she jumped on the couch, demanded to be petted immediately
and was purring really loud!
I think she just forgot she was supposed to be scared of us.
After that, she claimed my boyfriend's chair as hers and she spent the rest of the evening napping. Yup, she's totally the boss of the house now.
They gave her the name "Grizzle" at the SPCA, but we decided to change it to "Groseille" (French for gooseberry). It is pronounced something like... grow-zaye. She's a little chubby, so we'll need to keep her weight under control. That means I'll need to train my boyfriend, who tends to spoil pets way too much!
I'm so excited (can you tell?), we've been wanting a pet for SO LONG, I can't believe we finally have one.
Here's a picture of my chubby little girl!