HR director Bernard Glaser and director of production Michel Dheilly were taken hostage by workers at the tyre plant in a row over the factory's closure.
The company, which employs about 3,000 workers, announced plans in January 2013 to shut the factory, resulting in more than 1,000 job losses. Union group CGT had been negotiating with management for the past year.
The union wanted redundancy packages of between €80,000 (£66,000) and €180,000 (£149,000), as well as retraining assistance for 24 months, rather than the original offer of 15 months.
The action took place after a court rejected the union's most recent appeal against the factory's closure.
Local TV footage showed executives sitting at a table while workers shouted at them. According to the CGT union, the two managers had been given water and were allowed use of their mobile phones.
Evelyne Becker, a union representative, said the two had been prevented from leaving after a "stormy" meeting with staff.
Mickael Wamen, the union president, told French television: "Clearly it was no longer possible to keep fighting for our jobs, so we decided to change tactics and fight for the largest compensation possible."
The union said in a statement: "We just want to continue to work and not swell the ranks of the unemployed and marginalised, and if for that we have to resort to extreme methods, we won't hesitate to do that."
Goodyear has so far declined to comment.
'Boss- napping'
The capture of the two directors at the factory in Amiens marks a revival of the so-called 'boss-napping' that was prevalent in France at the start of the financial downturn in 2008 and 2009. This happened to companies including 3M, Caterpillar and Sony.
This prompted former French prime minister Nicolas Sarkozy to give police powers to intervene with force if necessary.
Although France has a penalty of up to five years in prison and a €75,000 fine for holding a person against their will for less than seven days, it is rarely enforced.
