what does she think of me?

I know this kind of question has already been posted many times but every situation is different I believe.

I'm an intern student in a very big Japanese company near Osaka. Because I'm working in the research and development building the people working here are all engineers so as anyone would expect there aren't many girls. My department of 40-50 people has only 3 girls. So among these three girls there's a very cute a nice girl. I met her with most of the others members of the group when my boss introduced me the other people from the department during lunch. He said that she can only speak Japanese and as I had just arrived in Japan I ended up just saying basic greetings and maybe a few sentences of broken Japanese.

A few weeks later there was a nomikai (as the Japanese tradition in the end of April for newcomers and stuff). On the way to go I was in the same group of people as her (I didn't plan to I just went with my boss since I don't know the place) and I tried talking with her a bit but I think we were both embarrassed about not being able to speak Japanese and English respectively. During the nomikai I couldn't talk with her because I was at the newcomer/boss table. When it ended people went in different groups and I went to the one where she was going (I was asked if I wanted to join by someone else) and I spoke a bit more to her, just small talk but it was nice, the alcohol helps talking in languages you don't feel fluent in.

A few days later I noticed that she was greeting me whenever we would met in the alleyway/elevator (I replied accordingly of course) but I didn't take it as any special meaning since it's just being polite. After a while I think she noticed that I was checking the time and stuff so that I would be more likely to "randomly" see her but she didn't seem to act any differently.

A few weeks ago one of my coworkers mentioned during lunch that he should invite her to make me come to an event he was organising (and that I didn't want to attend). I felt very embarrassed because I never mentioned her to him and his desk is too far for him to actually notice anything so I'm assuming someone else told him about it.

And a bit after that (that's the last part I promise) some other interns thought it would be nice to go together to some fireworks and invite some coworkers. I liked the idea so I sent a mail to invite some of my coworkers (including my boss and her) explaining them that we (the interns) decided together it would be nice to go to fireworks together. They all replied saying they were busy/didn't want to come except her so after almost one week I asked her in person about it and she apologised and said she really wanted to go (and looked happy about it) and thanked me for inviting her (in Japanese, note: I don't suck as much now). I'm also pretty sure she knows the other aren't coming because they often chat together and I think I overheard them mentioning fireworks.

So coming to the fireworks seems to me more than just being polite with me (just doesn't feel like she has to it's outside of work and other people already refused) and yet it doesn't seem like she's interested in me, before her reply I felt more like she was avoiding me and now I don't know. So what do people here think? I don't really hope to date her for now but I would appreciate some pointers to help me know her feelings so I don't mess up and make things weird at work. I think I would try to be friends first but how I can tell if she would want to be friends (I mean more than just coworkers speaking to each other)?

PS: Because I guess I will be asked this so I can as well put this now. I'm French, 21 and still need to do a few more years before I graduate (but it will be in Japan) and she's 25 or 26 (not sure since I didn't ask her but she hasn't been working here for long)

Without reading your ridiculous wall of text, the simple answer is just ask her.
No one hear can read minds, so it's best to talk with her personally.

Why don't you have the date first before you decide whether she likes you and you like her.

Note that she might not want to get involved with you since you work together, even if she likes you.

To ... the problem is that I try to talk to her as often as I can at work but people are pretty busy so I never get more than a few sentences of conversation. This is (at least for me) clearly not enough to tell anything. I'm not good at telling the difference between Japanese people just being polite and Japanese people being friendly.

I know I will get a much better idea after the "date" but the thing is it's not really a date because other interns are coming (with some workmates). I'm not sure how she sees it and how to act during that time (I'm not good at reading the atmosphere).

You will put her off with your giddy behaviour.....relax. You are 21 and new in Japan, don't get ahead of yourself.

I don't think you can force it. Better to date other girls as well until things become clearer.

I'm not going to try dating other girls. What would be the point? I'm always serious about relationships and trying to date someone when you already like someone else doesn't work.

I don't really see where you think I've been giddy. Until now I had just been talking to her a bit sometimes. I can tell we both feel uncomfortable when speaking to each other alone but I don't know if she feels that way because she can't speak English and doesn't know what to say to make me understand or it's because she feels something for me.

It's been more than 3 months already and in my opinion it's already quite late to make a move. I just used the first chance I had to invite her in an indirect way (to avoid asking to go somewhere just the two of us which would probably be too much at this point)