Sorry for the long read a TL;DR is featured at the end with a quick and simplified question. Please do read this if you have experience with French women!

Background

This semester I have a group project with four members where one of the members is an incredibly beautiful French foreign exchange student. Where I go to school there are a lot of French people and so I know quite a bit about French culture. The rest of the group is actually all French as well but this girl in particular is only here for the year. She is decent at english but still struggles in the most adorable way.

During our group meetings our legs have touched without anyone moving them and remained touching for a while. We have shared a computer when one of ours was dead twice and to keep my arm from jabbing into her I have put it around her or at least the back of her chair with both of us being very comfortable with the situation. I feel like all of our physical contact indicates each of us feels the same way about each other at least to some extent (more than her just being polite but rather that she wants me to be touching her).

On Tuesday we had our first group presentation and afterwards as a group we went out for drinks to celebrate. Towards the beginning of this outing the girls are up at the bar ordering drinks and me and the 27 year old gay dude were left at the table alone. First thing out of his mouth to me was "Sooooo you and [Her name]" indicating he thought we had hooked up or were getting pretty close at the very least. I told him I was interested and he was very encouraging saying that he was sure it would happen given what he had seen.

That night we all got quite drunk and talked about varying topics ranging from sex to smoking and drinking habits. All sorts of more intimate details of all of our lives. During some of the time I was very close to this girl and talking with our faces several inches apart and our legs touching. The whole night as well as every group meeting and class we have sat next to each other as a side note as well. By the end of the night I had walked her home (although I just said I was going to a friends near by and was happy to walk that way with her) and wanted to kiss her with every ounce of my heart but didn't want her to feel like I was doing it because we were drunk and discount it in any way since I feel really strongly for this girl. I ended up parting ways with her and feeling really good that all of us had such a nice night out together celebrating.

On to the questions

So from what I can tell I have set this whole situation up quite nicely, I am just trying to determine where to go from here. I have another meeting with the group tonight and would like to set something up for this weekend as to not drag out this whole will he wont he thing for her. If I could get any recommendations based on what I gave so far that would be great but as follows are some things I have been pondering.

Every time we go our separate ways me and this lovely lady have done the traditional kiss on each cheek (faire la bise). I wanted to know if it would be rude or uncalled for to, when we are saying goodbye tonight, go for a real kiss when we both go in for the cheek kisses. I feel this could be a breach of the tradition and be a little sneaky. Its a time when she would not be expecting it unless I made it clear looking into her eyes and advancing towards her lips slowly.

This could work but I'm afraid it could blow up in my face too. I am still tempted but need feedback. Also I wanted to ask her out to dinner tonight either to go tonight or maybe some time later this weekend. I just want to do it when we have our meeting to make sure I don't do it over the phone or text. Firstly I wanted any tips on the best way to ask her out (as I am accustomed to hook up first then going out is implied later) and secondly if by asking her out if that may change the kissing situation and make it more clear I will be going in for a real kiss to say goodnight.

I have a burning passion for this girl right now and just want to play my cards right. Plus I have to work on a project with her for the next several months so I don't want to fuck with the group dynamic or mess up any potential I may have with this beautiful girl.

Please Reddit help me fulfill this fantasy.

TL;DR Turning a cheek kiss into a real kiss and asking out a French foreign exchange student.