Ford Motor Co. said it earned a profit of $60 million in the second quarter, making a dramatic turnabout from the same period a year ago, when its losses totaled $468 million.

The improvement was even more noteworthy for Ford's hard-pressed North American operations, which lost $971 million before taxes in the April-June period a year ago. This year, the second quarter pre-tax profit was $31 million, a gain of nearly $1 billion. Pre-tax earnings worldwide were $104 million.

Ford chairman Philip Caldwell and president Donald E. Petersen noted that Ford's share of the U.S. auto market increased in the second quarter, led by sales of its Excort/Lynx subcompacts, which remain the best-selling car line in America, according to Ford.

The Big Three U.S. auto companies announced total sales of 154,385 during the second 10 days of July, a 7.7 percent improvement from the same period a year ago. The sales figures, combined with Ford's earnings report and Chrysler's announcement Wednesday of a $12 million second quarter profit, gave the industry something to cheer about after the worst sales results for May and June in 28 years.

But Ford's return to profitability, like Chrysler's, was due in part to an ambitious second-quarter production schedule. With a sharp sales slump in May and June, all of the American car companies are facing large inventories in dealers' hands, which will depress sales in the months ahead.

Outside the United States, Ford made a pre-tax profit of $73 million in the second quarter, including a loss of $28 million in Canada, compared with pre-tax profits of $407 million a year ago. Ford said the drop was caused primarily by sharp declines in sales in Great Britain and Argentian, following exchange rate changes those countries made to combat inflation.

Industry analysts expect that Ford will be back in the red in the third quarter and, with its $402 million pre-tax, worldwide loss for the first quarter, will finish the year losing money.

Caldwell and Petersen acknowledged in a statement yesterday that a return to profitability for Ford requires a recovery in auto sales, which slumped to depression levels in May and June after a spurt early in the year, when sales were boosted by offers of large rebates.

Worldwide sales of Ford products, including trucks and tractors, totaled $11.3 billion in the second quarter, up 21 percent from a year ago.

Ford said its cash position remained strong. The company had $2.8 billion in cash at the end of the second quarter, after repaying $985 million of short-term debt in the United States. Worldwide, its debt declined by $640 million in the first six months of the year.

But this cash conservation came at the expense of an apparent slowdown inits capital investment plans to modernize its car and truck lines and production facilities. In the second quarter, Ford spent $492.7 million on capital investments, bringing the total for the first six months of 1981 to $927.3 million, leaving itself a long way to go to meet its goal of nearly $2.5 billion to $3 billion for the year.

Ford's sales for the July 11-20 period totaled 36,753, up 14 percent from the 32,159 figure a year ago. General Motors' sales were up 2.7 percent, from 97,129 cars a year ago, to 99,793. The biggest gains belonged to Chrysler, which sold 17,839 cars in the mid-July period, 27 percent above the 14,037 figure in 1980.

So far this year, GM's car sales are 5 percent below last year's figure, Ford is down 4.3 percent, and Chrysler is 23 percent above the depressed levels of 1980, when the company was struggling to win government loan guarantees and avoid bankruptcy.