French President Francois Mitterrand's grim austerity program is beginning to bite, generating fears that instead of the millennium originally promised by the Socialists, there will be no escaping further hard knocks.

"I hear," says an anxious teletypist, "that they (the government) will try to slap on a wage freeze next year, but I can't believe the unions will stand for it."

Finance Minister Jacques Delors shocked the nation by forcing Frenchmen to cut down this summer on their traditional holidays abroad, so as to keep money at home. That caused a certain amount of teeth-grinding for Frenchmen who daily see the Champs-Elysee and the posh shops along the Rue St. Honore jammed with American tourists, loaded with dollars worth nearly 8 francs each after three devaluations of the French currency.

But now, with the August holiday finished, the worry has turned to taxes and wage restraints.

A wage freeze, as such, is not in the cards. But Mitterrand's planners do intend to try to limit wage increases--which had averaged close to 15 percent in 1981, 12.5 percent in 1982, and 10.5 percent this year--to no more than 8 percent next year.

From the workers' standpoint, however, an 8 percent pay increase limit would be barely enough to prevent "real" wages from declining, if Mitterrand's inflation target of 8 percent is actually achieved.

So far, the French have had much less success in lowering inflation than any big country in Europe, except Italy. For the 12 months ending in July, the cost-of-living index was up 9.4 percent. That, to be sure, is an improvement over recent 13.5 percent inflation peaks. But in the United States, West Germany, Japan, Holland and Switzerland, inflation rates have come down spectacularly to 2-2.5 percent.

Meanwhile, unemployment is at the politically unacceptable level of 2 million, or 8.3 percent, and, according to the Organization for Economic Cooperation and Development, is likely to rise. So it's easy to understand why Mitterrand's popularity has crashed; the latest poll this week showed only a 29 percent approval ratimg.

Mitterrand took to TV on Sept. 15 to appeal for public understanding of his new "rigorous" budget, which tightens the tax screws one more notch. Although his reasoned analysis and personal manner were persuasive to this foreign visitor in the comfort of a good hotel room, the reaction was critical, and some Paris papers dismissed his performance as "professorial."

It is clear that the French government knows it's got a hard sell on its hands. Government spokesman Max Gallo, in the same doublespeak that some of his American colleagues use, was able to announce 40 billion francs- worth of new taxes, and yet promise there will be no more "tax pistol-whipping" next year.

While the French public resents the Mitterrand program, the financial establishment abroad cheers it on as the only alternative to virulent French trade protectionism. The goal of the latest belt-tightening package is to cut government spending or raise taxes by a total of about 65 billion francs, the equivalent of 2 percent of French national output.

More significant, the Mitterrand program, as a Morgan Guaranty analysis points out, is designed to force a decline in cosumer spending. Thus, social security taxes are being raised (1 percent surcharge). In addition, most taxpayers will have to make a compulsory three-year loan to the government equal to 10 percent of their combined income and wealth tax in 1982. There also will be higher taxes on tobacco products, alcohol and gasoline.

If the austerity program works, it will cut the deficit in the budget to 3 percent of national product, and further slice the French trade deficit, which rose to the ominous total of $23 billion last year.

That's what foreign investors want to see --a deflationary program that will give France a chance of controlling its external accounts and regaining competitiveness in world markets.Mitterrand and Delors try to to saddle Washington with some of the blame for their economic mess. Trade Minister Edith Cresson last week told a New York audience that the overvalued dollar, a product of American "neo-protctionism," has exacerbated problems for France.

But the real test for Mitterrand is at home. He must ride herd on an uneasy coalition with the Communists, who will be measuring public sentiment while deciding whether to challenge Mitterrand (only two years into a seven-year term) by provoking industrial strife. Whether Mitterrand, like Reagan and Margaret Thatcher, can get away with a program that whips inflation by raising unemployment remains to be seen..