England’s victory ended France’s hopes of a Grand Slam as the reigning champions bounced back from their 40-24 defeat by leaders Wales last time out.
But it needed Itoje’s try four minutes from time to ensure victory, the lock forcing his way over for a score confirmed by the television match official.
“They’re being described as the best team in the world,” said Jones of France.
“And we said to our players before the game we’re going to be racing them to the World Cup.
“They are a good team, they’re developing, we’re developing, and it’s going to be a good race between the two of us. And we got a bit of a start on it today,” added Jones, who saw his England team beaten by South Africa in the 2019 World Cup final in Japan.
Defeats by both Scotland and Wales had effectively ended England’s hopes of a successful Six Nations title defence.
And they then saw France scrum-half Antoine Dupont score the opening try of yesterday’s match in just the second minute, with Damian Penaud also crossing before half-time.
But wing Anthony Watson marked his 50th England cap with a try and captain Owen Farrell’s boot kept the hosts in the game before Itoje capitalised on his side’s increasing forward dominance in the 76th minute.
The win was also a reward for England’s improved discipline.
Having conceded 41 penalties in the opening three rounds, with Itoje a prime culprit, they did not get on the wrong side of referee Andrew Brace until the 25th minute yesterday.
“Too many things went against us (in the Wales match), including our discipline and obviously that was a big positive today,” Farrell said.
“When we don’t give away as many penalties like that, we get a lot more of the ball, a lot more control over the game and I thought we showed what we could do off the back of that.”
The Saracens centre added England had not been spooked by France’s early try.
“We knew there was a long way to go in that game...It didn’t feel that we were shocked by that.”
Farrell added he had not needed to pass a message to his side in the closing stages.
“It felt like we were going to get a chance, not waiting for one - it felt like were going to make one.”
And as for Itoje being the man to take it, Farrell said: “He was at his best in a big game, which is no surprise for us.”
England complete their Six Nations campaign away to Ireland next weekend and veteran Australian boss Jones said: “We’re so disappointed we can’t defend our trophy so we want to make sure we finish the competition with a good feeling about where we’re going.”