Trains of SNCF are an obvious option. You can get there on direct trains from Paris (2 hours and something), Epernay (many trains, take just 1/2h). Buses might bring you to Troyes. Many other trains are also good options.
Reims is situated at 134 kms or 1hr and 5mns from Paris by motorway.
475kms.......3rs30mns from AMSTERDAM
270kms.......2hrs30mns from BRUSSELS
300kms.......2hrs20mns from DIJON
1200kms.....14hrs from FLORENCE
450kms.......5hrs from LONDON
265kms.......2hrs55mns from ORLEANS
950kms.......10hrs from SALZBURG
260kms.......3hrs from SARREBRUCK
420kms.......5hrs from WIESBADEN
Ease of access an hour away from PARIS. At the junction of major motorways A4 and A26, Reims is a metropolis of easy access, by car.
By plane, The plane attracted on the eve of the 20th century by the wide plains of Champagne, today puts the City of Coronations within reach of international airport. The airport of Reims Champagne hosts commercial aviation, the aerodrome of Reims Prunay is for business travellers.
By railroad, Reims should soon be 30 minutes away from Charles De Gaulle Airport, by the TGV Est.
I suggest getting around Reims by car. This way you can stop and see or do anything you wish to stop for. Some areas are great for walking too.
Reims is 134 North East from Paris, easily accessible by train or car.
If you want to discover the region of Champagne and the wineyards, you will need your own car.