Epernay is best reached by train. Direct services from Paris Gare de l'Est run several times a day and take about 1 hour 20 minutes; the same line continues to Reims (a 25-minute hop in the other direction) and on to Chalons-en-Champagne and Strasbourg. The station sits a five-minute walk from the Avenue de Champagne.
By car, Epernay is about 1 hour 45 minutes from central Paris via the A4 motorway, with the last stretch on the smaller D951. The TGV station of Champagne-Ardenne, on the LGV Est line near Reims, brings high-speed rail times from Paris down to under 45 minutes, but you still need a connecting train or car to reach Epernay itself.