As well as setting a new Premier League record for netting in 11 consecutive matches, the 29-year-old has scored 22 goals to help the Foxes be crowned champions.
Smith – who played for Leicester and England – thinks this could be a tournament where Vardy seizes the opportunity to make the most of what could be a limited period at the top of the game.
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Smith told Omnisport: "He is 29 and he has not got too many years at the top for a player who uses his pace and physical abilities
"But for the next two or three years, he is going to be a major force in the Premier League and hopefully for England at the Euros.
"He is definitely going to go to France - it is about how Roy Hodgson chooses to use him. He can ruffle quite a few feathers in France I think.
"He has got that hunger. We all know where he came from - non-league football - there is an element of making the very most of his time in the spotlight."