Even more than in Wall Street, there is an almost desperate hope in Europe that Democrats and Republicans in the United States will put common sense above politics, and quickly agree on a compromise to cut heavily into big budget deficits.

The bottom line here is that neither businessmen nor politicians have faith that an economic recovery can be sustained unless there is a surge in investment to replace antiquated European factories. Unemployment is shockingly high--and worse, it probably won't recede for at least two years or longer.

So, in the view of most of the international financial "establishment" that ferried this week between meetings in Paris and here, the key is to get high interest rates down. And in turn, that will require getting the American deficit for fiscal 1983 sliced by $80 billion or so, to a maximum deficit of about $100 billion.

Treasury Secretary Donald Regan has been assuring his opposite numbers in Europe that there will be a "substantial" reduction in the deficit--and his European listeners desperately want to believe him. Because American interest rates so closely affect European interest rates in an interdependent world, the investment boom that Europeans are so keen to get going--they believe--will never have a chance with interest rates so high.

The professional staff at the Organization for Economic Cooperation and Development in Paris is among the most pessimistic. Without some help from America, they believe that stagnation in Europe--with a concentration of unemployment among young people--can carry along to the end of this decade.

Naturally, all of this gloom and doom doesn't provide the happiest backdrop for the economic summit to take place early June in Versailles. As one high official said here, "We're groping around for some grand initiative that could be pulled out of the hat."

Presumably, businessman George Shultz, who has visited Margaret Thatcher and French President Francois Mitterrand and is on his way to the other heads of state in a pre-summit sweep for President Reagan, has the same objective.

In actuality, there are some highly regarded officials who depart from the pessimistic view, and who offer a highly favorable prospective scenario over the next couple of years. They see inflation staying down, further progress in moderating wage rates, and interest rates actually coming down significantly.

One influential central banker rejects the common view in Wall Street that interest rates are bound to resume an upward trend, once there is the first hint of recovery. "It's hard to see why interest rates must go up in a recovery," he said, "because they're already so high." He cites, as a precedent, the decline in the U.S. prime rate from a peak of about 12 percent before the 1974-75 recession to less than 6 percent in 1976 during the recovery.

But there's a big "if" to all of this: A recovery must get under way later this year in response to a genuine deal between Reagan and Congress on the budget that permits the Federal Reserve to lower interest rates.

On Capitol Hill, many Democrats have been trying to force the Federal Reserve Board's hand by putting a flat requirement for an easier monetary policy into any budget resolution calling for a reduced deficit. At the Fed, where the prayers for a lower deficit match those in Wall Street and Europe, they don't think any push will be necessary, once those deficit numbers recede.

But obviously, something has to happen soon. If an agreement isn't reached before the election, there is fear that the financial markets will conclude that the best chance has evaporated--resulting in incalculable psychological and real damage.