France is seeking to repair its badly damaged relations with Iran in a move officials here hope could lead to the release of four French hostages kidnaped by Islamic extremists in Lebanon.

Recent signs of a rapprochement between France and Iran have included the opening of direct negotiations on outstanding financial claims, an exchange of warmly worded New Year messages and a change of tone toward France in Iran's state-controlled media.

Any lasting improvement in Franco-Iranian relations would represent a significant diplomatic shift for both countries and could have repercussions throughout the Middle East, in the view of foreign policy analysts here. France's Socialist government has repeatedly been attacked by the government of Ayatollah Ruhollah Khomeini because of its military and financial support for Iran's enemy Iraq in the five-year-old Persian Gulf war.

The flurry of diplomatic activity between Paris and Tehran coincided with optimistic reports about the progress of negotiations for the release of French hostages kidnaped in Lebanon between March and May last year by pro-Iranian groups. The kidnap victims -- two diplomats, a journalist for the weekly magazine L'Evenement du Jeudi and a sociologist -- were reported to have been transferred to Syrian-controlled territory but their precise whereabouts are not known.

French President Francois Mitterrand this week confirmed that he had been in contact with Syrian President Hafez Assad about the hostages and hoped for their swift release. But he refused to go into details about the negotiations which, according to French officials, have reached a particularly "delicate" phase.

"We seem to be near a solution, but it could all still fall through," said Jean-Francois Kahn, L'Evenement's editor. "One element is the authorities in Damascus and Tehran. The other is the kidnapers themselves and they still seem to be holding back."

Kahn said that according to his information, a compromise had been reached on the main demands of the kidnapers. These include the repayment of $1 billion of confiscated Iranian assets, the adoption of a more neutral position by France in the Iran-Iraq war, and the release from a French prison of five men who attempted to assassinate the former Iranian prime minister, Shahpour Bakhtiar, in Paris in 1980.

A French Foreign Ministry spokesman confirmed that the Iranian demand for financial compensation was among the subjects discussed by a senior French emissary, Jacques Martin, during talks in Tehran earlier this month. The assets were confiscated by the Bank of France after the 1979 Islamic revolution when the new Iranian government backed out of a French-led nuclear energy consortium known as Eurodif.

French officials depicted the talks in Tehran as part of a general settlement of financial claims between Iran and France and insisted that they were not directly related to the situation of the French hostages in Lebanon. They also denied reports, circulating in western diplomatic circles, that France has agreed to supply arms to Iran as part of a deal on the hostages.

France's position as Iraq's second largest arms supplier after the Soviet Union has until now been a major stumbling block to any significant improvement in relations between Paris and Tehran. In 1983, Iran broke off all commercial and financial links with France in retaliation for the delivery of five French Super-Etendard aircraft to the Baghdad government and organized anti-French protests around the country.

A Radio Tehran commentary earlier this week welcomed a New Year message from Mitterrand to Iranian President Ali Khamenei expressing a wish for improved relations. But it went on to complain about French support for Iraq in the war and the tolerance shown by the French government to numerous anti-Khomeini exiles who have made Paris their base.

While France is not prepared to stop supplying arms to Iraq, it is eager to put an end to a situation in which it was exclusively identified with one side in the gulf war, according to foreign policy analysts here.

"The French government knows that it is impossible to resolve the hostage problem without reestablishing contacts with Tehran. It also wants to insure itself against new acts of Iranian-inspired terrorism," noted a French diplomat privately.

The French opening toward Iran, according to this analysis, has been made possible by a strategic judgment that the gulf war cannot be won by either side. As long as Iraq was in danger of losing the war, France wanted to prevent what it regarded as an Iranian threat to the pro-western Arab states along the gulf. Today, in the French view, that danger is less acute.

"The government strategy is to try to resolve the problem of the hostages by placing it in a broader political context," a French official said.

Of the principal conditions set by the Lebanese kidnapers for the release of their hostages, the one that appears to cause the French government most difficulty is the demand that Bakhtiar's would-be assassins be released.