Franchitti was raised in Whitburn, West Lothian, and educated at Edinburgh's Stewart's Melville College. His father, an amateur racing driver, introduced him to karting at a young age, and by the time he was in his teens Franchitti had won more than one hundred races and twenty karting titles, including the Scottish Junior Championship (1984), the British Junior Karting Championships (1985 and 1986), the Scottish Senior Championship (1988), and runner-up in the 1989 British Senior Karting Championship.
His single-seater career began in 1991 under David Leslie Racing, when he won the inaugural Formula Vauxhall Junior Championship. He joined Paul Stewart Racing (PSR) and finished fourth in the 1992 Formula Vauxhall Lotus Championship, then won the title outright in 1993 with six victories. PSR promoted him to British Formula Three in 1994, where he finished fourth with 133 points, a single win at Silverstone, and six top-three finishes. In 1993, he also won the Autosport BRDC Award.
Unable to fund a move to Formula 3000, Franchitti was signed by Mercedes-Benz for its junior programme in the German-based Deutsche Tourenwagen Meisterschaft (DTM) and the related International Touring Car Championship (ITC). He drove an AMG-Mercedes C-Class V6, the same machinery that fronted one of the most technically sophisticated touring car projects of the era.
In the 1995 DTM season, Franchitti placed fifth in the Drivers' Championship, scoring two pole positions, four podium finishes, and 74 points across fourteen races. His simultaneous 1995 ITC campaign was even stronger: he won his first touring car race at Mugello, finished twice second at Donington Park, and took third at Estoril, ending the year third in the Drivers' Championship with eighty points.
For the 1996 ITC season, Franchitti remained with AMG-Mercedes and improved to fourth in the Drivers' Championship with 171 points and five podium finishes, adding a race victory at the Suzuka round. The ITC folded at the end of 1996 due to escalating costs, ending Franchitti's time in touring cars and pushing him toward American open-wheel racing.
Franchitti debuted in Championship Auto Racing Teams (CART) with Hogan Racing in 1997 and quickly established himself as a front-runner. After joining Team Green in 1998, he won three races and finished third in the championship. The 1999 season saw him tie Juan Pablo Montoya on points but lose the title on the countback of race wins — Montoya having won seven races to Franchitti's three.
A serious pre-season testing crash at Homestead in 2000 caused fractures to his left hip and pelvis, plus minor brain contusions, which affected his form for the next two seasons. Franchitti moved to the Indy Racing League (IRL) with Andretti Green Racing in 2003, though a motorbike accident that April limited him to just a handful of events.
His breakthrough in the IRL came in the 2007 IndyCar season, when he won four races including the Indianapolis 500 — the first Scottish winner of the race since Jim Clark in 1965 — and clinched his first IndyCar Drivers' Championship, edging Scott Dixon in the final race. The following year, Franchitti attempted a NASCAR Sprint Cup programme for Chip Ganassi Racing but found the Car of Tomorrow concept ill-suited to his skills, and the team was disbanded mid-season.
Returning to IndyCar with CGR in 2009, Franchitti dominated, winning three consecutive championships (2009, 2010, 2011). His 2010 season included a second Indianapolis 500 victory, and 2011 ended in tragic circumstances when a 15-car accident on lap eleven of the season finale, which claimed the life of Dan Wheldon, was abandoned, handing Franchitti the title. He added a third Indianapolis 500 win in 2012.
On 6 October 2013, during the penultimate round of the IndyCar season at Houston, Franchitti's car made contact with Takuma Sato's vehicle on the final lap and was launched into a catchfence, tearing it apart and sending debris into the grandstands. Franchitti suffered two spinal fractures, a fractured right ankle, and concussion. Medical examination revealed that further major crashes would risk permanent paralysis and brain damage, and Franchitti announced his retirement from competitive driving.
In total, Franchitti competed in 265 American open-wheel races, winning 31 and reaching the podium 92 times.
Franchitti has served as a driver coach and advisor for Chip Ganassi Racing since 2014. He has co-commentated on the Formula E world television feed since the series' inaugural season that same year.
His honours include the BBC Scotland Sports Personality of the Year (2007), the Gregor Grant Award, the Jackie Stewart Medal, and an MBE appointed in the 2014 Birthday Honours for services to motor racing. He has been inducted into the Long Beach Motorsports Walk of Fame (2014), the Indianapolis Motor Speedway Hall of Fame (2017), the Motorsports Hall of Fame of America (2019), and the Scottish Sports Hall of Fame (2022).