F. W. Woolworth & Co., the variety store chain that is fighting off a takeover bid by Canada's Brascan Ltd., yesterday reported lower earnings for the first quarter ended April 30.

However, the drop in profit to 27 cents a share from 34 cents a year earlier was caused by a turnaround in foreign currency translations, the company said.

Net income of $8.78 million was after losses of $2.5 million on such translations in contrast with a gain of $10.86 million. Sales rose to $1.379 billion from $1.225 billion.

The results include those of its 52.7 percent owned British subsidiary.

Chairman Edward F. Gibbons explained that the British subsidiary's sales were strong during the quarter but the strength of British pound against the dollar cut the American parent company's equity in the British subsidiary's earnings by more than half. Gibbons said this could be recovered in the rest of the year if the foreign exchange market stabilizes.

Marshall Field & Co. sales and net income rose dramatically in the first quarter of 1979 compared with the first quarter of last year, the company said yesterday.

Sales climbed 34.6 percent from $141.9 million last year to $191.2 million this year. Net income jumped from $57,000 (1 cent a share) last year to $367,000 (4 cents) this year.

Angelo R. Arena, president and chief executive officer, said a number of factors contributed to the added sales, including three more selling days in the first quarter of 1979.

Also contributing to the increases were the addition since Feb. 1, 1978, of 10 department stores in Oregon and Washington, and 16 home furnishing stores in California, Nevada and Arizona.

Federated Department Stores Inc., the nation's largest department store chain, said that first-quarter 1979 earnings were $28.1 million (58 cents a share), an 11 percent increase over $25.2 million (52 cents) in the same quarter of 1978. Sales for thequarter were $1.2 billion, up 9 percent from $1.1 billion during the same quarter last year.

Chairman Ralph Lazarus and President Harold Krensky said in a statement the higher earnings resulted from "sales gains throughout our department store, mass merchandising and supermarket divisions."

Federated also said that its inventory position "remains at levels appropriate to sales."

Federated's 162 department and specialty stores include Bloomingdales and Abraham & Strauss, Bullock's, Burdine's, I. Magnin & Co., Lazarus, Shillito's and Rich's. It also operates 85 Ralphs Grocery Co. stores in California.