Travel times from Paris to Groningen (and return) by train can vary a bit. Prices start at 49 euros, up to 109 euros, for a one-way ticket. Most tickets cost around 58 euros. Travel times vary between 5 and 7 hours. (booking early up front via the website could be a good idea) Information can be found on www.nshispeed.nl/en
(The Eurolines busses do not go to Groningen from Paris in february. One could go to another city and then travel by train, but this does not seem very practical!)
Traveling from Giessen is possible by train. Travel times vary from 6 to 7:30 hours and costs vary from 39 to 99 euros, for a one-way ticket (booking early up front via the website could be a good idea. Information can be found on www.nshispeed.nl/en
Travel times by train vary from 3:14 to 4:08 and 4:53 hours in total. The shortest travel time requires a Thalys ticket, which is more expensive (total amount for a one-way ticket is around 90 euros, or 58 when younger than 26). The longer travel times cost 30 euros (adults 26-59) or 19,50 (younger than 26) for a one-way ticket. It is advisable to book tickets up front via the website. Information can be found on www.nshispeed.nl/en
There is the possibility to fly with Ryan Air from London Stansted to Bremen, Germany (and return). Prices vary depending on the time and day. The price per flight (without additional costs) is around 30 pounds. ryanair.com
From Bremen to Groningen (and return) one can go by bus (Public Express), this takes around two hours. Prices from 9 to 23 euros. www.publicexpress.nl/groningen-bremen/
There is also the option of flying to Eindhoven or Maastricht with Ryan Air (from Stansted). Travel time from these cities could be a bit more complicated/longer (by train) and a bit more expensive. The trains can also be very full, so the Public Express busses might be more comfortable. The flights are more or less the same prices as to Bremen.