Britain and West Germany have expressed support for French calls for a common Western European research project in high technology areas similar to those covered by President Reagan's Strategic Defense Inititiative.

The heightened interest in the French-led Eureka project, which emerged during visits to Paris by the British and West German foreign ministers this week, appeared to reflect growing Western European concern about the technological challenge from the United States and Japan.

In a speech today to the assembly of the West European Union (WEU), which is responsible for coordinating European positions on defense and security issues, West German Foreign Minister Hans-Dietrich Genscher said Europe should create a "technological community." He called for a "coordinated" European response to SDI, the space-based missile defense system also known as "Star Wars."

"Europe must not drop to the level of subcontractor and supplier. It must unite its technological capabilities so that it can be an equal partner of the United States," said Genscher, acting WEU president.

The West German's use of the word "subcontractor" was similar to warnings already sounded by President Francois Mitterrand about a Reagan administration invitation to Western European countries to join in SDI research. The French fear that Western Europe may not benefit fully from future technological advances unless it speaks to Washington with a common voice.

An apparent shift in the previously skeptical British position toward Eureka was revealed yesterday by British Foreign Secretary Geoffrey Howe in talks with French Foreign Minister Roland Dumas. Howe was quoted by British officials as saying Britain was ready to consider participation in the French-led project.

Both West German and British officials said they did not regard the Eureka project as incompatible with participation in SDI research as proposed by the Reagan administration. Mitterrand, on the other hand, has said France will not take part in SDI in "its present form."

The Eureka program was suggested by Mitterrand last month as a way of coordinating civilian European research efforts in such areas as lasers and particle beams, high-speed computers, and artificial intelligence. It was originally criticized by British officials on the grounds that it could lead to the creation of expensive new bureaucracies, and met with only a lukewarm reception elsewhere.

The project was widely viewed in France as a means of countering the technological and political challenge posed by SDI even though French officials insisted that it was not intended to be a rival to it.

By rallying around the French proposal on the understanding that it does not exclude participation in SDI, the other Western European countries are helping to paper over differences that have strained the usually harmonious relations between Mitterrand and West German Chancellor Helmut Kohl.

Mitterrand is to meet Kohl May 28 in Bonn in preparation for a European Community summit at the end of June.

Genscher told the WEU today that other Western European countries in the organization -- Italy, Britain, Belgium, the Netherlands, and Luxembourg -- also shared the opinion that Europe should strengthen its joint technological capabilities. He said WEU members would try to coordinate their response to SDI once each nation had decided whether to participate.

Yesterday, a British aide, Lady Young, said that, while Britain wanted to respond positively to the Reagan administration's invitation, it was also seeking clarification on practical questions and would closely consult with its European partners.