"Is that Mitterrand?" the woman asked as an official motorcade roared along the quai across from the Eiffel Tower. "No, it must be Andropov," replied the man standing beside her.

As Soviet leader Mikhail Gorbachev departed Paris at midday after a highly publicized four-day visit for talks with French President Francois Mitterrand, this scene was one small indication among many that his Parisian interlude did not make a particularly deep impression on French public opinion.

The polite, but distinctly reserved, welcome the French capital and its media gave the new Soviet leader was in striking contrast to the more informal and friendlier reception he received in London in December.

Here he seemed to make large strides toward persuading policy makers that they are dealing with a far different kind of man than his immediate predecessors, Yuri Andropov and Konstantin Chernenko.

But the French capital appeared to take the visit of Gorbachev and his wife, Raisa, with something of a shrug and at times with outright hostility, which surfaced in confrontational questioning by the French media and by public complaints about the extraordinary security precautions that shut down entire sections of Paris as his large motorcade moved around the city.

"We know that he came here to throw dust in the eyes of western public opinion and did not feel like helping him," said one independent but tough-minded French editor in explaining his newspaper's relatively low-key treatment of the Gorbachevs. "As for her, the French people who spent time with her say that she is not particularly interesting, despite the stylish dresses and what you read about her in London."

When they made their final appearance together yesterday at a two-hour press conference, Mitterrand did not give the impression of a man who would say, as Margaret Thatcher did last year, that Gorbachev was a man the West could do business with.

Mitterrand's rather weary explanation of his rejection of a Gorbachev proposal to involve France in arms control talks suggested instead that Gorbachev is a man with whom the West has to do business, but which it probably will not enjoy.

Many French analysts today found themselves wondering exactly how much business Mitterrand did wind up doing with Gorbachev in repairing the once badly frayed Soviet-French relationship. The initial balance sheet suggests that the two leaders agreed, at least implicitly, to put behind them the sharp rhetoric they have flung at each other over human rights, arms control, Afghanistan and Poland and other subjects.

Mitterrand, for example, did not tackle the subject of the continuing internal exile of dissident physicist Andrei Sakharov, as he did at a Kremlin dinner in 1984. He left that task for Prime Minister Laurent Fabius, who gave Gorbachev a list of individuals France would like to see receive permission to leave the Soviet Union.

He also appeared to go out of his way at the press conference to warn that President Reagan's plan for stationing weapons in space as a defensive shield could lead to an end to the arms control process, a position that carried strong echoes of the Soviet stance on this issue.

And his quick public acceptance of an invitation from Gorbachev to visit Moscow raised the possibility of a return to annual French-Soviet summits, a practice that Mitterrand had discontinued when he came to power in 1981, voicing strong condemnation of Soviet arms deployment in Europe and support for Reagan's nuclear rearmament program.

Mitterrand's aides insisted that the Gorbachev visit did not bring a reversal of official French distrust of the Soviets. They portrayed a slow evolution of Mitterrand's willingness to renew high-level dialogue with the Russians based on a changing balance of forces in Europe.

But the Socialist leader, facing a rising political challenge from conservative forces led by Gaullist politicians, did appear, either by design or by accident, to be prepared to move France more toward the "equidistant" policies carried out by Charles de Gaulle in trying to balance France between the Soviet Union and the United States.

Such a change was undoubtedly one of Gorbachev's major objectives in a trip intended to demonstrate to West Europeans and Americans his dynamism, relative accessibility and willingness to break with the past.

But reports surfaced persistently here that the Soviet delegation was unhappy with the relatively modest coverage given the ceremonial aspects of Gorbachev's first visit to the West as party leader.

When he arrived on Wednesday, for example, the daily newspaper Liberation covered its front page with one large photograph -- of actor Rock Hudson, who had died in California that day. Gorbachev's arrival was an inside item.

Much attention was devoted by the press to his substantive proposals on arms control, but that tended to be critical.

The effect was that of a very large pail of water splashing on a very old stone.

French officials who dealt with Gorbachev echoed a similar impression, while cautioning that they felt that the water would keep coming in an effort to wear away at the stone. They portrayed him as tenacious, determined and intelligent.

In his meetings with the French, Gorbachev acted decisively and quickly, giving only pro forma gestures to consulting colleagues in what is supposed to be a collective leadership, according to one authoritative account.

Part of the contrast in the London and Paris receptions lies undoubtedly in the sophistication with which the French capital treats such visits. Moreover, Gorbachev came to London as part of a parliamentary delegation and heir apparent, rather than as the top man.

He was thus able to mingle more freely and follow less structured programs in London. Also, some of the novelty of commenting on his quick grasp of western manners, in contrast to previous Soviet leaders, has worn off.

"He is a normal man," Michel Tatu, a leading Kremlinologist, wrote in Le Monde after speaking with Gorbachev at a presidential dinner. "That is the news."

But Tatu and other commentators were quick to acknowledge that Gorbachev's style and his proposals show conclusively that the wooden style and intimidating policies of former foreign minister Andrei Gromyko and the leaders he served have been put aside, at least for the time being and quite possibly forever.

There was no hint of the kind of bluster that Gromyko, who has been moved upstairs to the state presidency, showed when he threatened to turn the Italians into ashes if they accepted American missiles.

Instead, Gorbachev repeatedly emphasized that the Soviet Union shares a common civilization with Europe. When Mitterrand refused negotiations, Gorbachev softly said he was only suggesting a dialogue with France to try to find a way to reduce the risk of nuclear arms to the world.

There was no hint, as there could have been in the past, that Mitterrand was committing a criminal act to further imperialist policies by not listening to the much more powerful Soviet Union.

Some of his interlocutors came away from meeting Gorbachev with a sense that more was involved in this soft approach than a simple appeal to public opinion here and in the United States, although that element was certainly present as well.

For them, Gorbachev's proposals for regular contact between the Common Market and the Soviet Bloc economic grouping Comecon, and a mention of greater contacts between the Warsaw Pact and the North Atlantic Treaty Organization as institutions, suggested that he was significantly softening the previous Soviet insistence on dealing with Europe as a collection of individual countries that could be bent to serve Soviet purposes.

There were, these interlocutors reported, small seeds of a policy that would try to reposition the Soviet Union in some aspects as a European country, with a claim to a different kind of respectability.

This would be a far more subtle, and long-term, strategy than simply trying to use European public opinion to create problems for the United States and for NATO.

"He struck some of us as a man who takes a long view and who thinks he will have a lot of time to change the way the Soviet Union is viewed, and treated, in the rest of the world," one French source said after meeting Gorbachev.