The couple, who have been dating since 2011, wed in front of about 10 people in Mazan, Provence - close to where the bride's family has a holiday home.
Mayor Aime Navello told the Associated Press he married them at the town hall.
The short service was followed by a reception for family and friends, reported to have included Righton's bandmates and actress Sienna Miller.
Knightley, 28, announced her engagement to Righton, 29, last year.
"Keira was a charming bride, very modest and simple in her attitude, as was James," Mr Navello told the Daily Mail.
"I got the impression that it was a very moving experience for both of them."
The actress, who was Oscar-nominated for her performance in 2005's Pride and Prejudice, is the daughter of playwright Sharman Macdonald and actor Will Knightley.
She rose to fame in the British hit Bend it like Beckham, becoming an international star in films including Love Actually and the Pirates of the Caribbean franchise.
'More interesting'
Knightley also won critical acclaim for her performances in films such as Atonement, A Dangerous Method and, most recently, Anna Karenina.
Later this year, she will be seen in Jack Ryan - a prequel to previous Tom Clancy adaptations - playing Cathy Ryan opposite Chris Pine.
Singer and keyboard player Righton has performed with indie rock band the Klaxons since 2005. The group won a Mercury Music Prize in 2007 for their debut album Myths Of The Near Future.
In an interview last month, Knightley said she did not want an extravagant wedding day.
"We're not 'big wedding' types. I don't need to have all that. I'm just trying to enjoy the engagement bit.
"My parents are together after 40 years. The fights are there but they love each other.
"It's not like the first three months, the first two years... whatever it is, but I think it gets more interesting, or I hope so."

Transparency International accuses western governments, including the UK and the US, of ignoring corruption as a major driver towards terrorism, notably in the Middle East.
It calls on them to press far harder for accountability in military budgets.
The report comes as Iraqi forces advance on the IS stronghold of Mosul.
The report, entitled The Big Spin, argues IS took advantage of corruption to radicalise and recruit people, presenting itself as the antidote while ignoring its own dishonest activities.
"Corruption is a rallying cry, an enabler and a key modus operandi for IS," said Katherine Dixon, director of Transparency International Defence and Security.
"The failure to grasp this undermines efforts to tackle the rise of violent extremism.
"The international community expends great efforts tackling the 'ideology' of groups such as ISIS, focusing on the religious rhetoric they produce, yet completely ignoring the material circumstances in which they thrive."
Transparency International, which campaigns against corruption in governments, outlines a number of recurring themes used by IS to recruit people in its research.
In social media posts, it highlights systematic corruption - including nepotism and bribery - while presenting itself as a provider of security, justice and welfare.
It also plugs into a sense of discrimination felt by Sunni groups, and suggests the West and its allies are complicit in the corruption.
What's more, corruption has physically weakened some forces - like the Iraqi army, which did not have enough soldiers to combat IS when it first attacked Mosul because thousands of people were being paid, but not actually working.
Ms Dixon warns this means that without addressing the problem at the highest level IS will not be defeated.
In particular, Ms Dixon - who co-authored the report - said "what we shouldn't be doing is putting western taxpayers' money into helping create exploitative, predatory state forces".
"This is not just about closing off the corrupt channels that enable the day-to-day operations of groups like IS, but rethinking relationships with the Mubaraks [in Egypt], Gaddafis [in Libya] and Malakis [in Iraq] of the future," said Ms Dixon.
"Corruption is a real security threat, more than just a means for elites to line their pockets. In the end corrupt governments by fuelling public anger and undermining institutions, are the architects of their own security crises."
Actress Keira Knightley has married Klaxons star James Righton in the south of France.
[NEXT_CONCEPT]
So-called Islamic State (IS) will never be defeated unless the corrupt conditions that help it to thrive are addressed, a new report claims.