I did the same thing three weeks ago with a lot of luggage (we went skiing and brought our own equipment). Take the metro line D, entrance in Gare de Nord station (downstairs), two stops (Gare de Lyon) and exit in the station (upstairs). Yes, you will need to walk up and down stairs, but the distance is practically null.

The taxi will be more convenient, if you have a lot of luggage, but you run the risk that a traffic problem (not exactly unknown in Paris) will cause you to miss your train. The metro, in my experience, rarely has delays.