Chancellor Helmut Kohl's new Cabinet took office today and immediately saw its pledge to launch an economic revival collide with an announcement of the worst September unemployment figures in West German history.

Eager to set a new tone of fiscal austerity, Kohl told reporters at his first press conference that Cabinet ministers had agreed to take a 5 percent cut in salary as their personal contributions to a national belt-tightening agenda.

He said the gesture was meant to set an example of self-restraint before an Oct. 13 policy statement to parliament in which Kohl is expected to outline a program of social welfare cuts. "We will be demanding sacrifices from everyone in the government statement on Oct. 13 , and I think it is good that the Cabinet should set an example," Kohl stated.

Then, appearing buoyant despite the gloomy economic news of the day, Kohl flew to Paris for his first international encounter as chancellor -- a dinner tonight with French President Francois Mitterrand, whose economic headaches are considerably worse than Kohl's.

The lightning visit, arranged over the weekend, seemed intended to underscore the importance of German-French relations, which had been important to Kohl's predecessor Helmut Schmidt as a counterweight to U.S. leadership and as the core of Bonn's relations with Western Europe.

The prospect of a new German austerity under Kohl's center-right government has stirred apprehension in Mitterrand's Socialist France over potential damage to trade between the two countries and over a feared undercutting of the franc against the deutsche mark.

Kohl termed his meeting with Mitterrand a good-will trip in anticipation of an official visit to Bonn that the French president is planning to make later this month. Kohl said he intended to stick to the diplomatic calendar Schmidt had prepared, which includes summit meetings with French, British and Italian leaders during the next two months.

In a ceremony this afternoon in which Schmidt formally gave up occupancy of the chancellery building to Kohl, both men stressed the importance of continuity in foreign policy.

Asked about his government's expected new stress on ties to the United States, Kohl indicated this would not be done at the expense of relations with the East Bloc.

"We will be sound partners," he stated. "This means that we will be dependable partners, dependable as well in our relations with Central and Eastern Europe." Kohl said he wanted "sensible, if possible, good relations" with the Soviet Union as with all of West Germany's neighbors.

Kohl has made it clear, though, that his top priority will be boosting Germany's stagnant economy. The new coalition plans to revise the 1983 budget by enacting welfare cuts, tax increases and new business incentives by the end of the year.

Official figures published today showed that the labor market had deteriorated further after the summer holiday period, leaving a record 1.82 million people out of work in September, or 7.5 percent of the work force. The odds for near-term improvement also seemed to worsen with the publication of an industry federation paper reporting that about 50 percent of 14,000 companies recently polled said they planned to cut staff next year while only 5 percent envisaged hiring new workers.

Even so, the conservative Kohl has given signs that he will refrain from adopting Draconian measures. The 16-minister Cabinet sworn in today appeared to reflect the new chancellor's sense of balance between the liberal influence of his junior coalition partner, the Free Democrats, and the arch-conservative tilt of the Bavarian Christian Social Union, sister party to Kohl's Christian Democrats.

Highlighting the continuity theme, three of the four Free Democrats who served in Cabinet posts in Schmidt's left-center coalition have returned to the same jobs under Kohl. These are Foreign Minister and Free Democratic Party Chairman Hans-Dietrich Genscher, Economics Minister Otto Lambsdorff and Agriculture Minister Josef Ertl.

Reflecting the tensions within the new government, sniping between Kohl's two coalition partners continued today.

The presidium of the Free Democratic Party, under repeated attack from Christian Social Union Chairman Franz Josef Strauss who would rather not be partners with the Free Democrats, declared that Strauss would do better "to support the government and not permanently sow mistrust toward the new administration."

Answering for Strauss, his aide Edmund Stoiber called this demand "totally absurd" and reiterated the charge that the Free Democrats share responsibility for the political mistakes of the 13 years they governed with Schmidt's Social Democrats.