Franchitti, 41, from Bathgate, West Lothian, is one of the most successful British racing drivers of all time with four IndyCar championships and three wins in the Indianapolis 500 race.
He was forced to retire from racing in November 2013 after a serious crash at the IndyCar Grand Prix of Houston in which he suffered two fractured vertebrae, a broken ankle and concussion.
Speaking on BBC Radio Scotland, he described the lasting impact of the brain injury.
He said: “If I get tired, my concentration goes away. My decision-making isn’t as razor sharp as it was; I will repeat myself; my memory’s not great; I forget words.
“Faces – one of the side effects is I forget faces. You know you can sit there and think about somebody and what they look like and picture them in your head? I really struggle with that now.”
He said he still doesn’t remember the accident, adding: “No. I lost about five weeks in that one.”
Franchitti, who was married to Hollywood A-list actress Ashley Judd from 2001-2013, revealed the couple “wanted to go different ways” but insisted they remain close friends.
He also revealed he has found a new love.
He said: “Ashley was great, and Ashley was a fantastic supporter through big accidents, anything.
“Even after we got divorced, when I had my accident at Houston, I woke up the morning after and she was in the room with the dogs saying ‘right, here we are again, let’s get this fixed’.
“But we wanted to go different ways. We had different things we wanted to do in life.
“We are great friends. I’m very happy where my life is just now. I’ve got a wonderful girlfriend and I’m really enjoying it.”
The Scot also said he had not been comfortable with Hollywood fame during his time with Ms Judd.
He said: “We lived in Nashville on a farm. I stayed out of the Hollywood limelight wherever I could. That was never something I was comfortable with. That was something that had to be dealt with rather than something I wanted.
“I love the fact I can walk down the street here.” And he said returning to live in Scotland was “wonderful”.
He said “I lived in the most amazing place and had a great time but I was homesick for Scotland. I was homesick for as long as I was there, since 1999.
“It’s wonderful to be home, to be able to see my family, to be able to visit friends.”
Franchitti said speed has always “thrilled” him. He won the Scottish Junior Carting Championship in 1984, aged 11, then the British junior championship and the senior Scottish title.