It was the first time a Western head of state came face-to-face with the new Soviet leader, Konstantin Chernenko, to conduct affairs of state. And it came when conventional wisdom has it that East-West relations are in a deep freeze.
Not so, said French President Francois Mitterrand.
''There is no glaciation. We are not ice-bound at all.''
He was, of course, speaking of Soviet relations with France - not with other Western nations.
And while Mr. Mitterrand - despite outspoken criticism of the Soviets' treatment of dissident physicist Andrei Sakharov - apparently met with no outright rancor in the Kremlin, neither, it seems, did he find the Soviets ready for any sort of major breakthrough in East-West relations.
So Mitterrand left Moscow without agreeing to conduct regular meetings with Chernenko in the future, as had been the custom with past Soviet and French leaders. Future meetings, Mitterrand said, will occur when both sides have something to discuss.
With no ''glaciation,'' but no clear evidence of a thaw, either, what describes the state of affairs behind the Kremlin's walls?
One key Western analyst here suggests ''fragmentation.'' He posits that each member of the ruling Communist Party Politburo may be ''running his own shop, without too much overall direction.''
Such an analysis may help to explain some recent Soviet actions that seem puzzling to the West. During Mitterrand's visit, for example, Kremlin spokesman Leonid Zamyatin scotched the idea of a summit meeting between Chernenko and President Reagan - an idea Reagan had floated only a week earlier.
Thus, as one Western diplomat notes, the Kremlin reinforces its intransigent image in the West - and aids Reagan's efforts to appear conciliatory during this United States presidential election year.
That, of course, is hardly what the Soviets could have intended. - and is perhaps yet another example of a clear policy direction.
Western analysts here in Moscow assume the thumbs-down signal was primarily the work of Foreign Minister Andrei Gromyko, who they believe now runs Soviet foreign policy single-handedly. And Gromyko, they say, is still stung by the Soviet Union's failure to prevent the deployment of new NATO nuclear missiles in Western Europe last fall.
Consequently, they say, he is still pushing for a hard-nosed policy toward the US - and finding little opposition from any other member of the Soviet leadership, including Chernenko.
''They can only arrive at a consensus at a sort of low-level,'' says the Western Kremlin-watcher, ''one aspect of that being negativism toward the West.''
Does this ''low-level consensus'' mask an internal power struggle among the Politburo membership? Not necessarily, according to some Western analysts.
''I don't see any real struggle of ideas or personalities,'' says one. ''Inevitably there's a certain amount of maneuvering.'' But he suggests it might simply be a way of marking time.
In such a scenario, Chernenko - nominally the country's top leader - may actually be confining himself to ideological pronouncements and overall Communist Party policy, notably the drafting of a new party platform.
The other two major figures in the Politburo, Gromyko and Dmitri Ustinov, respectively, oversee foreign policy and defense.
The so-called ''middle echelon'' in the Politburo, veterans such as Moscow party leader Viktor Grishin, for example, content themselves with the present state of affairs, having no real incentive to go on a reformist bent.
And the younger members, notably Mikhail Gorbachev, continue to consolidate their own power, all the while watching for potential allies in their own eventual bids for greater influence once the older men leave the political scene.
In particular, there is now much speculation here about Gorbachev's standing in the Politburo. Although he is officially No. 2 in the Kremlin hierarchy and heir presumptive, there is no clear evidence that he is expanding his influence in foreign affairs, in the style of the late Mikhail Suslov.
Gorbachev was named head of one of the two foreign affairs commissions of the Supreme Soviet, this country's nominal parliament, during its last session. Still, ''we really haven't seen him do that much more in foreign policy than he did before,'' as one analyst notes.
Gorbachev apparently did not play much of a role during Mitterrand's visit; he did not take part in any of the private sessions with Mitterrand or the French government ministers accompanying him. He was, in fact, less prominent during the visit than Geidar Aliyev, another younger Politburo member.
If there is, in fact, ''fragmentation'' in the Politburo, what does that mean for Kremlin policy toward the West? In the short term, according to a number of analysts here, probably no major changes.
And in the long run? The answer, like future French-Soviet summits, may well have to wait until, as Mitterrand said, both sides have something to discuss.