Vie de France Corp., the McLean baking company known for its croissants and French breads, plans to acquire Country Epicure Inc., a maker of cakes and European pastries based in Katonah, N.Y. Vie de France officials declined yesterday to disclose the cost of the transaction, which is not yet final.

Separately, Vie de France said it had a profit of $689,000 (7 cents a share) in the first quarter ended Sept. 19, on sales of $17.2 million. Profit for the same period a year ago was $810,000 (8 cents) on sales of $14.7 million.

Vie de France has spent the past 15 months focusing on its basic bread and croissant business after running into financial difficulties when it attempted to expand too quickly. Richard J. Sharoff, the company's president, said it now is in better shape and is able to handle a broader product line.

"We feel that doing this will allow us to use our sales and distribution system to its full effect," he said of the acquisition.

The pastries will be sold in Vie de France's 58 stores around the country and will help Vie de France build its customer base in New York City, where Country Epicure is well known, Sharoff said.

Country Epicure was founded about 10 years ago by a husband and wife team and sells its fancy cakes, pies and tarts mostly to fine restaurants, retail gourmet shops and grocery specialty departments, Sharoff said. Country Epicure had sales of more than $6 million in the year ended in April.

Vie de France said that while its first-quarter profits were down from a year earlier, the quarter was the most profitable in the past 12 months for it. The increase in overall sales came mostly from the company's restaurant business, which is not yet as profitable as its wholesale bakery business, Sharoff said.

In other corporate earnings reports: Danaher Corp., a Washington company that manufactures and sells tires, vinyl siding and other industrial and rubber products, said it earned $5.5 million (24 cents) on sales of $207.6 million in the third quarter. Earnings for the recent period were up 127 percent over the corresponding 1986 period, when profits were $2.4 million (12 cents) on sales of $143.4 million.

The company attributed the increase to improved results in some segments of its business and the reduction of debt in connection with the acquisitions in the past year of Western Pacific Industries and Chicago Pneumatic Tool Co.

For the first nine months of the year, Danaher's earnings were $19.2 million (86 cents), up 137 percent from $8.1 million (40 cents) a year ago. Sales for the 1987 period were $588.5 million, more than double the $292.4 million of a year ago. Atlantic Research Corp. of Fairfax yesterday reported earnings of $5.6 million (60 cents) in the third quarter, up 51 percent from $3.7 million (42 cents) for the same quarter last year. Sales of $103 million were 12 percent higher than the $91.8 million in revenue for the diversified technology company in last year's third quarter.

The firm, which is one of the country's largest manufacturers of solid-propellant rockets, said that for the first nine months of this year, it earned $14.3 million ($1.55), up 13 percent from $12.7 million ($1.41) for the same three quarters of 1986. Revenue rose 12 percent to $300.5 million from $269.3 million during the first nine months.

Atlantic Research said the reasons for higher profits included increased sales of electronic products, higher margins in rocket motor production and lower operating costs following a restructuring last spring. Versar Inc. of Springfield had first-quarter earnings of $449,000 (12 cents), down slightly from $451,000 (17 cents) for the same quarter last year. Sales were $13.9 million, an increase of 40 percent over 1986 quarterly revenue of $9.9 million, the company said. Versar provides scientific and technical services on environmental and health and safety problems caused by toxic substances.