would be held to the letter of an 11th-hour deal in which he agreed to preserve threatened jobs at the plant in northeastern France and to provide 180 million euros ($235 million) of investment over the next five years.
The accord was concluded on Friday night, hours before a deadline after which the government had threatened to nationalise the plant.
It emerged on Monday that Arnaud Montebourg, the industrial renewal minister who had issued the nationalisation threat, was so disappointed with the terms of the deal that he had threatened to resign before being talked out of it by Hollande.
The president on Monday played down divisions in his cabinet, instead turning the focus back onto Mittal.
"The entire government is behind this accord and wants to see it implemented and respected," Hollande said.
"All the force of the law will be brought to bear if it is not."
But according to industry experts, the fine print of the 'deal' struck with Mittal bore little difference to what his company ArcelorMittal had always planned.
"There were no significant concessions," said Guy Dolle, a former boss of Arcelor.
Jean-Louis Pierquin, another former director of the group, added: "Mittal is only implementing his initial plan.
"The 180-million-euro investment would have been made in any case -- it adds up to 36 million euros a year, which is not that different to the 30 million a year they have spent on the plant for the last seven or eight years."
Dolle said the absence of a redundancy programme was also an illusory victory for the government, as staff numbers will be whittled down by natural wastage.
"It wasn't necessary given the age profile of the staff," he pointed out.
Pierquin agreed: "No redundancy programme does not mean that jobs won't be eliminated."
ArcelorMittal has said it will be negotiating with unions to allow for some workers to leave on a voluntary basis and the government has conceded that the total number of jobs at the plant may fall due to early retirement/redundancy deals.
At the heart of the row between the company and the government was the future of two idled blast furnaces on the site, which Mittal wanted to close.
The weekend agreement ensures they will be kept in a mothballed state which, theoretically, means they could be reopened quickly and the government has talked up plans for a potential conversion to a more environmentally friendly use.
Mittal however has only agreed to delay temporarily a definitive closure of the furnaces and the conversion depends on EU financing. If that is not forthcoming, the full closure will go ahead.
The confrontational stance adopted by Montebourg in the row with Mittal -- seen in India as having xenophobic overtones – prompted criticism from business leaders that potential foreign investors in France would be deterred by the prospect of government meddling in company decision-making.
On a visit to Paris on Monday, British business secretary Vince Cable highlighted a significant difference between the way Mittal had been treated in France and Britain's relationship with Tata, the Indian company which owns much of the British steel industry.
"Tata take a long-term view and we are very pleased with them," Cable said. "The problem is there is massive overcapacity in the steel industry so there is going to be contraction.
"We would encourage producers to do it in as humane and thoughtful a way as possible but there is not point attacking them for it."