Freddy is the Romantic Interest. In another play, he might have a big part. In this play, he barely has a part at all. There's not much romance to be found. Freddy's not exactly a heartthrob, though. When we first meet him he's running around looking for a cab…which he never finds. In Act 3, he mistakes Eliza's normal Cockney speech – the stuff about influenza and "doing in" – for "small talk." He thinks she's the bee's knees, and quickly falls in love with her. He wants to walk through the park with Eliza…but she'll have no such thing. Still, he leaves the party – and the play – in high spirits.
If anything, Freddy shows us how unconventional Pygmalion really is. There's not much room for your standard love affair in there, not with all the heavy stuff. He's another bit of comic relief, and, as we see in the last act, blackmail material for Eliza.