The midfielder, 29, who made only nine league starts for the Reds last season, joined the French club despite interest from several Premier League sides.
He told BBC Sport: "I've won everything in England and had a successful career.
"In 10 games I'll be back playing my best football and I see no reason why I won't get back in the [England] team."
Cole collected the last of his 56 caps when appearing as a second-half substitute in England's 4-1 defeat by Germany in the second round of the 2010 World Cup.
Later that summer, he
moved from Chelsea to Liverpool,
signing a four-year contract, however he struggled to make an impact at Anfield and played in just 11 Premier League games last season.
Aston Villa, Tottenham and Queens Park Rangers were all interested in signing Cole during the summer transfer window, but he elected to join Lille who will be playing Champions League football this season.
"This offer excited me," he told BBC Sport's Dan Roan.
"It looks a great club. They did the
[French league and cup]
double last season and I wanted this experience to test myself in the French league.
"Ever since I was a young lad, I wanted the opportunity to play abroad.
"It's a good opportunity to learn a new language and take in a new culture. We're all excited," he added, referring to his wife and baby, who are moving to France with him.
Cole admitted that it had been a "difficult 12 months" at Anfield but he had no regrets about moving to Merseyside.
"It didn't work out at Liverpool and I can't fault them one bit," he stated.
- 2011 (loan)
"I wouldn't blame anyone. There are many reasons and I knew from fairly early on that things would be difficult
"Roy [Hodgson, former Liverpool boss] is a good manager, he's proved that, but it just didn't work.
"I make decisions for the right reasons and you can only decide whether it's been good, or bad, at the end of your career.
"I might have a cracking season out here that leads on to something else.
"You can't think too long-term in this game, things happen in the blink of an eye but as it stands it's a season-long loan so let's see how it goes for everyone concerned."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.