Gaston and Gigi enter the Ice Palace, a large indoor skating rink with multi-level balconies filled with finely-dressed Parisians sitting in couples and groups. Everyone's drinking and gossiping and eavesdropping and watching.
This is Gigi's first time at an ice rink, and she's watching all the people as Gaston orders her a barbotage and a champagne for himself.
Liane is skating with her teacher, a handsome young man.
Gigi asks Gaston not tell her grandmother she's come to the Ice Palace, since such a pastime isn't "serious matter."
The film cuts back to Liane, still skating and completing a little turn with her handsome teacher.
Gaston asks Gigi what she thinks of Liane. Gigi says she's pretty, but common. Gaston seems embarrassed, but as he's about to respond, Gigi runs off, saying it's time to go.
Gaston's left to greet Liane, who's finally done skating. The teacher stands by the table, waiting for a tip, and Gaston slips him some coins and continues his conversation.
Liane says the man is a good teacher, but so "conceited, so superior in an inferior way." She can't stand him. Right.