Reims is located at a crossroads on the European motorway network between Paris and Strasbourg on the A4-E50 and between Calais, Troyes, Dijon and Lyon on the A26-E17. It’s about an hour from Paris to Reims by car. To avoid huge traffic jams, don’t travel around Paris at peak hour or return on a Sunday afternoon/evening.
Hop on the Eurostar from London to Paris and catch one of the frequent daily train connections (roughly one every hour) from there to Reims (45 minutes).
France’s train network is excellent, meaning it’s not hard to get around the bigger cities and towns. But the best way to explore the vineyards and champagne houses – which is the big reason to visit Champagne – is by hire car. It’s best to rent a hire car in Reims and drive from there, rather than renting in Paris and dealing with that city’s crazy traffic.