Defense Secretary Caspar W. Weinberger flies home from here Tuesday after four days of hard sell of a mysterious product to skeptical Europeans.

The product is President Reagan's Strategic Defense Initiative, or "Star Wars" plan. It is a $26 billion research program, aimed at finding ways to destroy nuclear missiles before they could hit the United States or Europe.

In peddling SDI face-to-face and over television since arriving here Friday, Weinberger has not been able to say what it might look like, when it might be delivered, how much it might cost, or even if it could work.

The Soviets say it would open a new round in the arms race, and Europeans fear that it could lead the United States to forget about the defense of Europe.

Weinberger moved to allay these reservations partly by telling the Europeans they could have part of the lucrative research work.

U. S. officials said that this offer found the French simultaneously attacking SDI and inquiring how they might sign up for the research money. "The French cannot be bought," said one U. S. delegate to the Wehrkunde Conference in Munich who heard their twin arguments, "but they can be rented."

The French dilemma is even deeper than it looks. Allied pursuit of a new missile defense, successful or not, is likely to push the Soviets to improve their own defenses to the point where they could stop French nuclear missiles, western experts say. So the French in working on SDI might be undercutting the credibility of their own nuclear offense.

The SDI has generated other contradictions in Europe, which Weinberger and fellow drummers have been spotlighting the last four days. Opponents contend that the United States would be tempted to hide behind a successful missile defense and leave Europe to fend for itself. But Europeans used to argue, administration officials noted, that an America vulnerable to Soviet missiles would not defend Europe for fear of losing New York, Washington and other cities. A vulnerable and invulnerable United States cannot both be Fortress America.

Besides, the administration's SDI salesmen asked, how can a Europe which is counting on the United States to defend it object if the United States also explores ways to defend itself?

But for all the salesmanship this week, U.S. officials concede the Reagan administration, and perhaps its successors, still has these hard questions before it:

How can the administration make good on its introductory offer of letting North Atlantic Treaty Organization partners join in SDI research without losing secrets and jobs to NATO nations which Congress would rather keep at home?

How can the administration shore up the shaky political support for continued spending on land missiles, like the MX, at the same time it is ballyhooing a missile defense?

How can the administration avoid sounding contradictory as it hails its missile defense as good for the world while condemning the Soviet antiballistic-missile effort as menacing?

How can the administration attack the strategy of relying on mutual assured destruction to deter nuclear war without at the same time strengthening the arguments of peace groups that nuclear weapons are immoral and should never be used?