Train travel Amsterdam to Milan

Have you considered flying? The train takes well over 12 hours. EasyJet and Vueling fly from Amsterdam to Milan for 40-50 euros. Check skyscanner.net and input your travel date to see the price. The flight is less than 2 hours.

Gare du Nord to Gare de Lyon is much too far to walk. The best way for any cross Paris journey is the métro, in this case the RER (express métro) line D.
See here: http://www.seat61.com/Paris-metro.htm#Metro%20routes%20from
There is even a video to show you how. It will cost a mere €1.80 per person.

Tickets, always at the company running the trains, Amsterdam to Paris: https://www.thalys.com/
Paris to Milan: http://www.sncf.com/

But, for a trip that long, if you aren't planning to spend any time in Paris or anywhere else en route, I would fly direct.

As a previous poster said, take a plane to Milan. They're cheaper and you'll get there in two hours.

Thanks for the information flying seems to be the smart choice , Is the scenery by train along the trip between Amsterdam and Milan very interesting, it will probability be our only chance the see France, Thanks Pete

I did this trip last year in the opposite direction from Turin. The part from the Netherlands to Paris is nothing to write home about, but one or two hours from Paris the landscape becomes very nice, and gets wonderful when the train crosses the Alps.
The RER is indeed the way from Gare du Nord to Gare de Lyon. It takes some 10 minutes with one intermediate stop. You've got plenty of time to do it. (Keep the ticket with you. You need it to open the gate on leaving the métro platform to the station concourse.)

I also recommend flying. But note that on some dates you can leave an hour earlier (8:00 a.m.) and make a single train connection at Basel, without changing stations. Either way, mountain scenery is only a couple of hours out of the 12+ hour trip.

The route through Basel is just under 12 hrs with only one change - in Basel. It goes through western Germany & Switzerland.