For further insight you might want to pull up two of my Forum posts: "Same Sex Kissing" and "Things Every Man Should Do at Least Once". An easy way to do this is to click on "other posts" next to my name. This will bring up all of my Forum posts and my recent comments on others' posts.
Yes many, probably most, straight men would probably freak out at the idea of French kissing a guy. But there is movement in this direction. See my Forum post. Some, not many but some, straight men now greet each other with a kiss. And members of the Hell's Angels Motorcycle Club have been doing it for decades.
Moving on to your girlfriend, you cannot let her dictate how you run your life. If an occasional man-on-man contact is important to you, then you've got to be able to do it. With or without her permission. It would be nice if she could join you in this and you could have a nice MMF three way, but if she won't, you'll just have to go it alone. If she cannot accept this, then she's not the girl for you.
And pleas do not try to smother this desire. It will not go away and if not satisfied, it could drive you to doing risky things. Let it happen in a safe and controlled way.