Despite France losing to Sweden in their final Group match, Gullit believes that they will progress to the semi-finals at the expense of the tournament favourites.
Gullit, writing on Laureus.com, says: "I have a feeling - don't ask me why - that France are the dark horses of this tournament.
"Forget what happened against Sweden - I just think they have the players capable of going a long way in this tournament and that includes beating Spain.
"I don't think Spain have missed David Villa as some have suggested - they have other forwards who can come in and do the job.
But again, other teams have analysed how to play against them and their Group matches were closer than may have been the case in years gone by. Spain will have to be on their toes and I am tipping France to edge this one."
Gullit believes Portugal will beat the Czech Republic this evening (Thursday) and that Germany will beat negative Greece as long as they maintain their discipline and remain patient.
Gullit, who played 66 times for Holland and lifted the European Championship trophy with Holland in 1988, will also take a keen interest on Sunday's quarter final between England and Italy, two nations where he enjoyed much of his career.
Gullit, who played for AC Milan and Sampdoria in Italy and played for and coached Chelsea and Newcastle in England, added: "England have nothing to lose against Italy.
"Expectation may have grown as the tournament has gone on, but they have done well and not having that huge pressure on their shoulders is working in their favour.
"Wayne Rooney had an easy goal but the player I have most been impressed with is Steven Gerrard. He has been superb and shown what a great player he has been.
"Italy will be more defensive as is their mentality but they also have some great players such as Andrea Pirlo. It's too close to call which way this will go."