After a couple of nights in Paris, grab a train back to London to make your flight back home. For the last night in London I recommend staying in a hotel near the Heathrow Airport. This allows you to get a taxi that will drop you off directly at your gate, and grab a last minute local cup of coffee.
The main thing to remember is to decompress and have fun. Ask locals their favorite spot to grab tea. Eat food that you’ve never tried, and if you get lost on the tube — get off at a random stop and explore the area.