What is the best way to travel to London and Paris if you live south of Paris?

I'm a study abroad student, and I have two long weekends in May. For the first weekend I would like to tour London, and for the second weekend I would like to tour Paris. How do I book this trip? Do I travel by train? What train station do I want to go to? Where/When do I buy the tickets? I'm pretty much clueless when it comes to this.

Also how much would all of this cost? I live in Nantes.

It depends where you live. Where south of Paris do you live? If it's in the suburb, you'd most likely take the m茅tro or RER:
http://www.ratp.fr/
http://www.transilien.com/web/site/lang/...

If it is in another region, you would take the train:
http://www.voyages-sncf.com/leisure/fr/l...

To go to London, you'll take the Eurostar train from Paris or a plane if you are near an international airport:
http://www.eurostar.com/FR/fr/leisure/tr...
http://www.opodo.fr/billets-avion/

If you give me your exact location I can give you a customized itinerary.

EDIT: I found a direct flight from Nantes to London through Opodo with Ryan Air for 130 鈧?the May 1st weekend. Going to Paris from Nantes can cost as little as 22 鈧?if you book early (60 to 90 days ahead). You'll have to wait a few days before you can book for May. You'll be arriving at Gare Montparnasse in Paris. For all prices, check the links I gave you above. Keep in mind that those 4-day weekends in the spring are busy travel dates, so they tend to be pricier. Prices change all the time, so it depends on when you book and what dates you travel. Check this site too:
http://www.tgv.com/EN/

The way most people get to London is through the Eurostar line, which runs through the Channel Tunnel from Paris. You could also take trains or buses into Paris. If there's a bus station in the town that you're staying in, they will most likely have information about cost, booking tickets and you'll be able to do all that there as well. And, since you are a student, it wouldn't hurt to ask the French students with whom you're studying what the best, cheapest options are for traveling throughout Europe.

Hop on a train