By John Irish

PARIS (Reuters) - France's opposition UMP conservative party won three by-elections on Sunday despite its own internal problems, in the latest sign of trouble for Socialist President Francois Hollande.

A six-week-old row over who won a November 18 vote for the UMP leadership has plunged the opposition party into disarray, but it finally looked to be capitalizing on the government's difficulties over the weak economy.

It won three by-elections, including a seat previously held by the ruling Socialist party.

"These elections constitute a setback for the government which has reacted so badly to the crisis and the risk of recession and promised too much to the French people," said Francois Fillon, a popular prime minister under Hollande's predecessor Nicolas Sarkozy.

It also looked as though a tentative deal between Fillon and contested UMP chief Jean-Francois Cope had been struck to hold a new vote for the party leadership during 2013.

NEW LOWS

Approval ratings for Hollande and Prime Minister Jean-Marc Ayrault hit new lows in December, a poll showed.

Hollande's government has faced criticism over the tactics it used in a two-month battle over the future of ArcelorMittal's Florange steel plant, which unnerved investors in the euro zone's second largest economy and confused France's unions.

His administration is also struggling to stop a haemorrhage of industrial jobs while curbing public spending and raising taxes to slash debt against the backdrop of a stagnant economy.

The president's backing slipped by four points to 37 percent in December, the worst rating since he became France's first Socialist president in 17 years in May, according to an IFOP poll published for weekly newspaper Le Journal du Dimanche.

Prime Minister Ayrault, who reached an agreement with ArcelorMittal to save jobs late last month, but was criticized over how the process was managed, saw his ratings tumble eight points to 35 percent, dipping below Hollande for the first time.

IFOP's deputy managing director Frederic Dabi said only former president Jacques Chirac had recorded lower ratings at the end of his first year in power with 30 percent in 1995.

"They are paying for the crisis, falling purchasing power, rising unemployment..." he said. "There is disappointment on the left and extreme venom on the right. Their (government) methods are causing anger."

The IFOP poll showed Hollande and Ayrault losing popularity among far-left voters (down 13 and 17 points respectively) and green voters (a 6 and 11-point fall).

Hollande has repeatedly said public criticism would not divert him from his goal of reviving the economy and has called on voters to judge him in five years.

With unemployment at 14-year highs of 10 percent, there was clear political advantage for Hollande to lock horns with Indian steel magnate Lakshmi Mittal to save the plant.

But the result was at best a no-score-draw, and the tactics used - anti-business rhetoric and the threat of nationalization - could damage his wider reform effort.

While his pugnacious, micro-managing predecessor Sarkozy led from the front, Hollande lets his ministers lead the fight, creating confusion over who runs industrial policy.

(Reporting By John Irish; Editing by Stephen Powell)