Private talks here and in Paris have strengthened Defense Secretary Caspar W. Weinberger's belief that relations with Sweden and France, particularly on military issues, are growing warmer.

Weinberger left Paris Thursday convinced that the Socialist government of Francois Mitterrand, two Communists in the Cabinet notwithstanding, will be one of the Reagan administration's staunchest allies on military issues.

Weinberger felt he had made progress on several fronts in those first face-to-face discussions with his French counterpart, Defense Minister Charles Hernu, an aide said.

While Weinberger acknowledged during his press conference in Paris Thursday that the Mitterrand government will fill the military orders Libya had placed with the previous French government, French officials predicted that there would be "technical problems" delaying some of the deliveries to Libya's Muammar Qaddafi.

"Technical problems are something that by their very nature cannot be announced in advance," one American official said wryly.

Hernu also agreed with the Reagan administration's view that neutron warheads must be produced to counter the Soviet edge in tanks threatening NATO forces, Weinberger said. Also, to reassure Weinberger that France appreciated the need to do more to answer the Soviet threat, Hernu gave Weinberger a peek at the new French military budget in the works.

"Very impressive," Weinberger said afterward. The American defense secretary in turn showed Hernu how Reagan intends to counter the Soviets strategically by deploying the MX missile, a new submarine missile and by building a new bomber. Those plans were applauded by Hernu, according to Weinberger's account. In Sweden -- despite an anti-Weinberger demonstration on his arrival -- officials went to great lengths to welcome the American defense secretary and assure him that their country's neutralism requires military strength.

The objective, Swedish Defense Minister Torsten Gustafsson explained to Weinberger in one of their discussions, is to train enough soldiers and to deploy enough guns to convince any would-be aggressor that Sweden would be no pushover.

To give Swedish defenses more credibility, officials here told Weinberger, the Swedish Air Force must have a new fighter armed with the latest air-to-air missile. No problem, Weinberger replied, as long as Sweden tightens its security on technology to minimize the chance that an American designed 404 engine or Sidewinder AIM9L missile would fall into Soviet hands.

The Swedish reportedly agreed to this, apparently clearing the way for a closer U.S. relationship with this neutral country.

What the new Swedish fighter should be is the principal topic of discussion here, with the choice between a domestic design or the U.S. F16 or F18.

A nuclear-free zone encompassing all Scandinavian countries plus Iceland -- as has been advocated for many years, particularly by Sweden and Finland -- was only touched on during Weinberger's discussions, and U.S. officials are convinced that it will not become reality, sources said. Swedish officials instead emphasized their resolve to strengthen defenses.

With the apparent aim of projecting this resolve to the rest of the world as well, Sweden laid on an elaborate travel schedule to show Weinberger -- the first American defense secretary to visit Sweden in an official capacity -- in Swedish military settings. Reporters and television camera crews were cordially invited to come along.

Yesterday, for example, many television watchers saw the American defense secretary walking along the catwalks at the Swedish Navy's mountain stronghold at Musk. The base was carved out of the mountain of solid granite standing alongside a deep natural water channel. Destroyers and gunboats practice racing from the channel right into the heart of the mountain via the deep canals blasted out of the rock.

Today Weinberger was flown from base to base, again with television crews in tow, to watch the Swedish Viggen fighter and the Swedish infantry in action.