Amadio said that after four hours of talks overnight with JLG management and a local government mediator, the company had offered to pay $42,000 per laid-off worker on condition that the workers return to work on Monday.
Pierre Martin, the mediator, said the workers will have two options, a plan allowing them to receive job training in other fields and receive $35,000 in severance, or opt out of the plan and receive $42,000.
The 53 workers will be officially laid off on September 28.
Laurent Wauquiez, the French employment minister, described the blast threats as "blackmail".
But the government has stopped short of sending in police, saying it understands the distress of workers hit by the recession and suggesting it sees the radical tactics as a media stunt rather than a serious threat.
The explosion threats are the latest tactic by disgruntled staff following a wave of "bossnappings" in which French workers took their managers hostage over factory closures.
On Thursday, Renault, the French car manufacturer, refused to meet the demands of workers at New Fabris, a bankrupt car-parts supplier, who threatened at the weekend to blow up gas canisters inside their factory in Chatellerault in western France.
Workers at the company want Renault and PSA-Peugeot Citreon, another French car producer, who account for 90 per cent of their business, to pay $42,000 to each of the 366 laid-off employees.
Both the car companies have said it is not their responsibility to pay compensation to the workers.
Renault offered on Thursday to buy up the stock of parts that were intended for it, and for the proceeds to be paid to New Fabris workers, but unions rejected the offer, which they estimated at $4,200 per head.
Laid-off workers at Nortel Networks, a telecoms firm near Paris, made a copycat threat on Monday, briefly threatening to blow up their factory before backing down the following day and obtaining a resumption of talks with their management.