The leaders of France and West Germany agreed today on the need to establish a European research program for space and advanced technologies but failed to reconcile their conflict over participation in President Reagan's Strategic Defense Initiative.

Following more than three hours of talks at the lakeside resort town of Constance on the Swiss-German border, French President Francois Mitterrand admitted that he and Chancellor Helmut Kohl were still taking "different roads" in their approach toward joining the American space-based defense program.

At the Bonn economic summit earlier this month, Mitterrand declared that France would not accept a role in the so-called "Star Wars" research project as now conceived.

The French rejection startled the Kohl government, which remains inclined to accept a U.S. invitation to join SDI research but wants to formulate a joint European position.

France is urging its European partners to pool their resources in a common program known as Eureka to bolster civilian research in high-technology sectors and prevent an accelerated brain drain of scientists and technicians toward the United States.

Britain and West Germany, after voicing some initial skepticism, have become increasingly interested in some kind of joint research program that would enhance Europe's prospects for future economic competition with Japan and the United States.

Kohl told reporters today that he shared Mitterrand's conviction that "it is vitally necessary for Europe to develop its own potential in high- technology fields."

The chancellor said French and West German ministers in charge of research and technology would meet within two weeks to devise an agenda of possible European projects. A commission of scientists, economists and administrators from both countries would determine the feasibility of the proposals, Kohl said. He added that all European countries would be welcome to join the program but that Franco-German cooperation would serve as its basic foundation.

Kohl's comments indicated that his government might ultimately become involved in both the SDI and Eureka programs, even though senior policy makers in Bonn have warned that West Germany could not afford to support both.

A top-level delegation of government and industry specialists is scheduled to visit Washington soon to discuss a research role for West German firms.

Kohl has said in the past that his government feels the SDI project is "worthwhile and justified" but that he wants assurances that West Germany will be able to share fully in the research findings. He noted today that "a whole row of open questions" must be answered before the Bonn government could approve participation in SDI.

Mitterrand has repeatedly expressed doubts about U.S. willingness to accept European countries as equal partners in the SDI project. At the Bonn summit, he said his intuitions were confirmed during a private meeting with Reagan when he heard the U.S. president refer to Europeans as SDI "subcontractors."

Moreover, France is worried that its own nuclear deterrent force, now being modernized at huge expense, will be jeopardized if SDI leads to more sophisticated forms of antimissile defense or more advanced offensive weapons to overcome such a shield.

"The interests of our two countries cannot be identical in all circumstances," Mitterrand said after today's encounter with Kohl. "That is in the nature of things."

The chancellor also underscored the differing security interests behind the Bonn-Paris split over the SDI program. "France is a nuclear power and we are not. France is not part of NATO military structure, but our role in the front line of the defense of the western alliance is irreversible," Kohl said.

Both leaders emphasized the importance of close Franco-German ties as the essential basis for greater progress toward European unity. Kohl said he and Mitterrand hoped the next summit of European Community leaders in Milan at the end of June would take "important steps toward political union."