Train from Krakow to Paris

It's a long ride - see the possibilities at www.bahn.de, and perhaps www.seat61.com will be handy to see travel conditions if you're a novice. Easiest route seems to be via Vienna and Frankfurt. Perhaps break the trip somewhere to avoid going mad.
International train prices in Europe are hard to research as they depend on so many factors (timing, single/return, your age, route, comfort...) , especially one like yours that crosses many borders. Let's state that flying is probably going to be cheaper. If you have time/money you could plan the route to take in some good landscapes, though Austrian and Switzerland for instance.

I agree with Jaroen that going by train is not the cheapest option. However, if you prefer to stay on the ground, you can buy the interrail ticket and use it for various national trains. You only need to pay for the seats and travel on one ticket.
http://www.interrail.net/
Price depends on the period of time and number of stops.

I would advise doing some research on the bahn.de website

One good option would be to catch a train from Krakow to Berlin (for which you can buy the ticket in Poland, but the German railways' site will give you approximate prices), and then continue to Paris either with a cheap flight (for instance with EasyJet) or with an overnight train (you could buy your ticket in advance on bahn.de for a discounted price), or with a series of daytime trains allowing you to break the journey in Cologne or Strasbourg (or even Brussels or Amsterdam)

Another option might be to go by train to a place like Bratislava (which is very convenient for visiting Vienna) and then fly Bratislava to Paris (if you can find a cheap deal on SkyEurope)

A third (even more unorthodox!) option would be to catch a cheap flight from Poland to the UK (there are plenty of possibilities) and then (assuming you have pre-booked long in advance on the Eurostar website, as cheap one-way fares are not easy to find) a train from London to Paris

It really depends on what cities/countreis you would like to see on your journey, how much time (and money) you have to make overnight stops, etc

If you decide against the train, you can avoid #3's unorthodox option via London by flying direct Krakow to Paris on Easyjet.