It's an eight-minute journey on RER line D, which is quicker than the metro. You use metro tickets for either.
Both Gare du Nord and Gare de Lyon are large stations, so allow plenty of time to walk between platforms.

Definitely the RER D. One metro ticket will cost 1.50€ (or 1.60€ from July 1st 2008 -- any ticket bought before that date remains valid indefinitely).

Thanks GeoffHamer and kerouac for your replies. Just one more point - is it unrealistic to walk between Gare du Nord and Gare de Lyon within the time frame?

Daktari

Not that I would walk that distance but how big is your luggage ?

Yes, it is unrealistic, albeit technically possible for a really fast walker. Gare du Nord is in the North of Paris, and Gare de Lyon is next to the river. www.mappy.fr actually gives the pedestrian time as 1h07. Want to jog with your luggage?

I've walked many times with luggage from Austerlitz station (across the Seine from Gare de Lyon to Gare du Nord and an hour would be good if you knew exactly how to go (fairly straight forward but still)

One begs the question since there are about hourly trains Gare de Lyon to Avignon you put yourself in such tight straights - and if you are arriving by train at Gare du Nord your train could well be a tad late IME

Thanks again for your replies. I won't have heavy luggage and enjoy walking, but your replies have convinced me to abandon this idea.