Basil has fleas. They're biting us. Are we completely screwed?

Please tell me these horrible flea-biting dreams will stop. Yes, yes, I know I need to give him a flea bath (first I need to trim his claws). I’ll probably give him frontline that isn’t expired.

But I need to know that I’m not going to have to burn everything in my house. What else should I do?

Good news—no carpeting.