Speaking Tuesday to reporters while campaigning in the state of New Hampshire, Bush said that it was wrong to criticize the French when attempting to make an issue of Republican rival Marco Rubio's poor Senate voting record.
"I made the mistake of saying that the Congress operates on a French work week," Bush said, according to Time magazine.
"I really did a disservice to the French," he added.
"I now know that the average French work week is actually greater than the German work week," Bush said.
"So, my God, I totally insulted an entire country -- our first ally -- that helped us become free as a nation! And I apologize. That did a huge disservice to France. It didn't really get to the magnitude of the problem: Three-day work week."
France played a key role in the US war of independence in the 18th century.
Florida Senator Rubio -- who like Bush hopes to steal the lead from current frontrunners Ben Carson and Donald Trump -- has come under fire for the perception he has neglected his duties as he focuses on 2016.
In a heated exchange during the October 28 Republican debate, Bush verbally slapped Rubio over his attendance record.
"Literally, the Senate, is it a French work week?" Bush asked. "Just resign and let somebody else take the job. There are a lot of people who are living paycheck to paycheck in Florida."
Many see Rubio as the most serious establishment challenger beyond Bush to face Carson or Trump, neither of whom have held elected office.
Rubio responded by saying that many White House hopefuls had missed Senate votes as they focused on the presidential race.
The day after the debate, the French ambassador to the United States, Gerard Araud, wrote on Twitter: "In any country, electoral campaigns offer the opportunity for a lot of bombastic nonsense. Let's be indulgent."
He added: "A French work week of three days? No but a pregnancy paid leave of 16 weeks yes! And proud of it."
Bush was Florida governor from 1999 to 2007. He is the brother of former president George W. Bush (2001-2009), and the son of former president George H.W. Bush (1989-1993).