The Channel is likely to be lumpy in January. There is one ferry company - P&O - left who take foot passengers. Train to Dover, long hike or taxi to docks, unpleasant entry to boat according to a recent review on this website, 90 minutes of not much unless you get a view of the white cliffs, an unpleasant disembarkation according to the same review, a difficult journey on foot or unlikely taxi to the station in Calais, an infrequent train to Paris.
Eurostar is easy, warm, dry, fast and painless. And is currently on sale on the Eurostar site. But sale or not, get your tickets asap because they get very expensive if bought close to departure day. They go up and never go down.