The England captain failed to score as the Three Lions lost 2-0 to Belgium in the third place play-off on Saturday, but struck six times in his six games in Russia.
That total puts him two ahead of Cristiano Ronaldo, Romelu Lukaku and Denis Cheryshev.
French forwards Antoine Griezmann and Kylian Mbappe both scored in France’s 4-2 victory over Croatia on Sunday to have four each.
Kane equalled Gary Lineker’s 1986 Mexico World Cup record for the number of goals scored in a tournament by an England player.
Lineker is the only England player to win the Golden Boot.
Kane scored in each of his first three games at the World Cup, with a hat-trick against Panama.
Speaking after the defeat against Belgium, the Tottenham striker said: “It shows we had a very good group stage, scored a lot of goals.
“I’m disappointed I couldn’t get a goal in the last few games. We will see tomorrow. If I do it it’ll be something I’m very proud of.”
Didier Deschamps captained France to victory in their first World Cup final in 1998 and on Sunday joined Brazil’s Mario Zagallo and Germany’s Franz Beckenbauer as the only men to have won the World Cup as both a player and a coach.
Croatia, led by coach Zlatko Dalic, had their dream dashed by France for the second time in the World Cup.
France clawed back from a goal down against Croatia in the 1998 semi-final to win 2-1, before going on to beat Brazil in the final.