The issue is more him checking out other women right in front of her in a way that makes her feel inadequate or at least unattended. If it’s that obvious to her that he’s doing it, he’s also probably doing it in a way that the women he’s staring at will notice.

Dunno if it’s a break-up worthy offense, but it’s probably not great for her self-esteem and communicating that to him is a good move. Maybe not with the champagne bottle though.