There are a couple of cafes once inside the eurostar terminal at st pancras but choice is limited. Definitely buy food and drink at the station before going through, you have loads of choice incl. M&s, pret, pain quotidien and lots of other stuff. Food on eurostar is disgusting and massively overpriced. Some french trains have food, some don't. It depends on the kind of train. It's never very nice though ime.
Trains in France really depend on whether you are travelling on SNCF (localish trains) or TGV/Thalys (high speed long distance). SNCF tend not to have food, TGV/ Thalys tend to have food. Have you already booked your tickets? As changing in Lille you have no need to change stations to get on the TGV, whilst in Paris you have to get from the Gare du Nord to the Gare de Monparnasse.
Sadly we couldn't go through Lille as the connections didn't work for us so we're having to go through Paris and change for Montparnasse. We think we've got that sussed so hopefully it should go ok.
I was concerned about the food because we've travelled to France before by plane and due to delays and connections etc we had nothing to eat from when we got up in the morning until we finally arrived over 12 hours later since they don't serve food on planes anymore. I'm determined that this time I will arrive in France having had food on the way there.