Travel time by taxi would be about 10-15 minutes once you're in the cab -- it's pretty much a straight shot on the boulevards and no river crossing, with Republique and Bastille being the places where you get hung up a bit. The queues to get a taxi at Gare du Nord can be long, so you might need to add up to 15-20 minutes to the total time.

My best guess at the fare would be €10-15, but that's an informed guess more than an experienced answer.

If you don't have much luggage, it's a fairly easy subway ride on the D line of the RER train (2 or 3 stops, no transfers -- about 15 minutes total, including walk, wait, and ride times). However, if you're not staying in Paris and don't have any subway tickets, you'd have the additional ticket-buying hassle.