Next up is the quarter-finals and a meeting with the defending champions.
After cruising through the last-16, Kane is under no illusions as to the challenge his side will face on Saturday.
"It was a solid performance, we took our chances," he said of the 3-0 win. "France are a great team, they’re reigning world champions. It's going to be really tough evening."
The skipper's first-half goal was a first at the tournament and he was delighted to break his duck.
"I had so much time, the ball just sat up nicely, the connection was perfect," he added. "I had a chance before that which I should have done better with, so it was nice to see that one go in.
“I'm a striker, so whenever I score I'm always happy."
Kane also offered support for Raheem Sterling, who missed Sunday's game after a robbery at his home in London caused to him to return to the UK on the eve of the match.
"Our thoughts are with him and his family," Kane added. "It's a private matter. It's never easy to see a teammate and a friend have to deal with something like that."