In the Falklands war, the French-made Exocet missile emerged as a terrifying killer that sank the British destroyer Sheffield from 20 miles away and threatened to turn the tables in favor of Argentina.

Now the Exocet is engaged in a more peaceful battle in Canada. The opponent is McDonnell Douglas' Harpoon missile, and the prize for the victorious arms manufacturer is tens of millions of dollars in contracts to build the new generation of electronic, sea-skimming, antiship weapons.

But the competition is unusual, given the changing rules of the game that govern the world arms trade.

The United States, increasingly concerned about controlling access to the new electronic weaponry, has put strict limits on where the Harpoon can be sold, since the missile is capable of striking targets "over the horizon" with deadly accuracy from more than 70 miles away.

"If you don't have good air reconnaissance, you'll hit anything that's floating around with this missile--and that rules out a lot of countries," one U.S. official said. The concern, he said, is that the weapon will fall into incapable hands or those that could use it against U.S. ships.

The Harpoon has been sold almost exclusively to politically stable, close U.S. military allies such as Japan, Israel and members of the North Atlantic Treaty Organization. A sale to New Zealand is pending.

An earlier sale of the weapon to Iran before the shah was deposed came as "quite a shock" to McDonnell Douglas and State Department officials and is cited as an example of risks involved in such transfers. Twelve of the 220 missiles originally ordered by the shah are estimated to have been delivered and apparently are in the hands of the Ayatollah Ruhollah Khomeini's government.

More recently, U.S. officials have refused to permit Harpoon sales to Taiwan or any countries in South America. The U.S. government controls sales under the foreign military sales program, so the Pentagon, not the commercial manufacturer, is the seller.

The Taiwan decision is particularly grating to McDonnell Douglas, whose representatives the Taiwanese approached about the missile three years ago at the Paris Air Show.

The Carter administration, then seeking to cement relations with Peking, subsequently refused to allow the company to discuss technical data on Harpoon with the Taiwanese. The company has not relaxed these restrictions.

But because France, Italy and Israel do not adhere to the same restrictive policies on selling electronic missiles comparable to the Harpoon, the race to obtain these weapons has rapidly expanded to dozens of Third World countries.

The Exocet, produced by France's Aerospatiale, has been marketed aggressively in such trouble spots as Libya and South Africa as well as Argentina. A consortium led by the French and Italian arms companies, Matra and Oto Melaro, has sold the Otomat missile to Libya, Egypt, Peru and Venezuela.

And Israel Aircraft Industries reportedly has sold its Gabriel, a sea-skimmer with a 22-mile range, to such countries as Taiwan, South Africa, Kenya, Singapore and Malaysia.

U.S. officials acknowledge that this creates a potentially dangerous arms race and say the United States "wouldn't sell to countries like Libya and South Africa."

However, they note that European arms companies could not exist financially without such Third World markets, since European arms procurement alone would not provide enough business.

The U.S. arms industry, which exports more than $10 billion worth of weapons annually, depends on such foreign markets for about 5 percent of its total sales, compared with 20 to 30 percent for French and British firms.

On the other hand, sale of new conventional weapons such as the Harpoon is beneficial not only to U.S. companies but also to military services overseeing weapons development.

As Capt. Eugene L. Geronime, the Navy's Harpoon project manager, said in a presentation this year:

"Foreign military sales of Harpoon lower the cost of hardware to the U.S. Navy, improve our balance of payments, provide tax benefits, create 10,000 jobs and recover over $150 million in research and development funds."

McDonnell Douglas, which designed the missile and integrated the various systems, has sold $1.5 billion worth of Harpoons.

Since 1976, the United States has ordered 1,800 of the new missiles, which range in price from $500,000 to $700,000 apiece, depending on whether they are rigged for launch from planes, ships or submarines. Foreign governments, which pay slightly more, have ordered 1,200.

In Canada, marketers of Otomat, Gabriel and Exocet have approached shipbuilders with proposals for including their missiles on six new frigates to be delivered to the Royal Canadian Navy.

Two competing shipbuilding firms are due to present final proposals, including a missile system, for the new frigates in October.

Indications are that Harpoon has advantages in this battle. The Canadian Navy is reported to be nervous about becoming dependent on a supply of missiles from the other side of the Atlantic.

Pratt and Whitney Corp., the U.S. company that makes engines for some McDonnell Douglas planes, owns 49 percent of one Canadian shipbuilding company, Scan Marine, Inc., of Montreal.

The other Canadian company, St. John Shipbuilding Co., of St. John, New Brunswick, is subcontracting combat systems for the frigates to Sperry, Inc., the U.S. company that produces the command-and-launch system for ship-launched Harpoons.