We are on a cruise that stops a Ville Franche. Is it feasible in one day to see both Monaco and shop Cote D' Azur using the local trains for transport?

Yes. There's train service (or taxi)from Villefranche to both Monaco & most all the towns along the coast. In the summer, these trains run very frequently.

A taxi in Villefranche is very expensive and very limited in number. It is an easy train ride to Monaco. What exactly are you shopping for??

Nothing in particular. I want to see Monaco, and my wife wants to shop in Cote D' Azur. So I want to make sure it is feasible to do both in one day.

More info. From my recollection there are shops (high end designer) near where you get out of the train station in Monaco. The typical tourist sights (palace, aquarium etc.) in Monaco are on "the rock" so to maximize time, I'd take a taxi to get there from the station or wherever you shop.

For other shopping without straying too far from the ship, go to Nice (there's a Galleries Lafayette) . If your wife is a serious shopper, I'd suggest splitting up-let her go to Nice & you go to Monaco. Or scrap this plan & both go to St Paul de Vence where there's lots to see and lots to shop.