traveling to London & Paris

Actually the Europeans don't like the term Chunnel. They call it the Eurostar Train. Discount tickets go on sell about 12 weeks prior to departure date and go rather quickly. Do book ASAP. You also MUST have checked in AT LEAST 30 min. prior to departure time- NOT JUST BE IN LINE- but ALREADY CHECKED IN. Do so get to the station rather early as lines can be long. You have to go through an airport like security check.

The fastest way to travel between the two cities is via the chunnel train. If you're going city center to city center there is no reason to fly unless you need to be at one of the airports for a connecting flight to somewhere. The train uses airline style pricing, so the sooner you book the cheaper it will be. Book ASAP at the official site: http://tinyurl.com/chunnel-train

Above is good advice re Eurostar from London to Paris, but I think your question is about flying. Yes, save money and time by flying open-jaw, from Tampa to London and returning from Paris to Tampa. Look on kayak.com or some other site for the "multi-city" option and plug in your cities in order. It's not a round trip, but it shouldn't cost much more, if any more, than a round trip. It will save you the half-day Eurostar return to London, trip across London to Heathrow, etc. I just checked kayak.com for flights from Tampa to London on August 13, and Paris to Tampa on August 20, picking the dates at random. It showed a $1081 fare on American via Chicago to London, and via Boston and Miami back to Tampa. Or a $1336 fare on US Air via Charlotte both ways. And many others. When you've seen the options, pick the airline with the best choice and book through its website. You should get the same fare, with a better chance of being notified and protected if there's a cancellation or other change. Have a good time!