Despite rumours, there is no wifi (wireless network) on Eurostar trains yet. That would be quite useful because due to the speed, the cell phone network keeps disconnecting.
At least there is free wifi in the London St Pancras station.
Wifi in Paris Gare du Nord is not free, you have to buy some prepaid cards from SFR (the French Vodafone partner) or pay online. It seems like you can get a free voucher if you travel in Business Premier or if you have a Carte Blanche, but as usual, I never spend enough time in the station to have time for this.
See a related comment about using cell phones on the Eurostar.