Former Treasury secretary G. William Miller has formed a new financial firm here that will engage in what Europeans call merchant banking--finding investment opportunities for clients, matching entrepreneurs with investors and making its own investments in budding new companies.

Miller said his firm, G. William Miller & Co., will not serve investors who are interested merely in building or increasing a portfolio of stocks and bonds.

"Our focus is to help build enterprises in the United States, either on domestic companies or international companies investing in new operations or extending their operations here," Miller said. "There will not be a great deal of effort on United States companies that wish to build abroad."

Before becoming President Carter's secretary of the Treasury, Miller was chairman of the Federal Reserve Board, the only person in U.S. history to hold the nation's two top governmental financial posts. Before he was named to the Fed, Miller was chairman of Textron Corp., a large conglomerate based in Providence.

Miller said he does not think locating the firm in Washington--rather than in the traditional financial centers such as New York or Chicago--will be a disadvantage.

For many of his firm's clients--especially foreign investors--a Washington location is an advantage, Miller said.

"They think the political capital is important. They are concerned not only with business and investment plans, but with the political climate, economic policies, exchange-rate and interest-rate policies," he said.

Miller declined to identify his backers or the amount of capital the firm has at its inception. He formally opened its doors Jan. 1, although he had been engaged in similar ventures since leaving office in January 1981. He said some of his clients--he has about 20 now--are likely to become public in the months and years ahead.