I agree with Ken about taking the RER D directly from Gare du Nord to Gare de Lyon (one stop at Chatelet-Les Halles). Trains run every 15 minutes and the actual ride takes 8 minutes. (The 14-minute estimate includes the time it takes to walk from the surface to the RER station and back to the surface again.) The fare is €1.60.
IF you arrive on time at Gare du Nord and IF you already have your tickets for Paris-Bern so you won't have to stand in line to either buy them or retrieve them at a ticket window and IF you don't barely miss one train and have to wait 15 minutes for the next one, then you'll make it. IMO, that's too many "ifs"--and you have no control over your arrival time at Gare du Nord. Take the later train.