Cole said playing in a foreign country for the first time had given him a fresh insight into the game and he wanted to bring that to Liverpool.
"I loved the football and we had a successful season," he said, having helped Lille secure Champions League football with a third-place finish.
"I'd always wanted to play abroad and sometimes you think the chance to do so at a good level may have passed by, but it was great and I really enjoyed the experience.
"I love my football, I love training and I love learning - and I did learn a lot out there.
"It opened my eyes to a new way of approaching football and the continental way.
"I'm always trying to learn, pick up new things and improve myself. I strive to get better every day."