At its best, counterfactual or “virtual” history (to use Harvard historian Niall Ferguson’s term), the exploration of what might have happened if history had not taken a certain turn, can be a fascinating intellectual exercise, a “what if” that illuminates what did happen. Unfortunately, “Virtual JFK: Vietnam if Kennedy Had Lived,” which begins a two-week run at Film Forum tomorrow, is neither fascinating nor illuminating.

Helmed by first-time director Koji Masutani, and featuring Brown University professor James Blight (previously known for his work on “The Fog of War: Eleven Lessons From the Life of Robert S. McNamara”), this new documentary is, at least superficially, devoted to the question of whether President Kennedy would have extricated America from the Vietnam conflict long before it could spiral into the quagmire that, under his successor, it became.

Despite the best efforts of Oliver Stone, that’s an old debate that can never be resolved. This film adds little to it other than artfully selected news footage, some interesting audio recordings of discussions within the Kennedy administration, and an inordinate amount of wishful thinking. The filmmakers examine the foreign policy crises that defined Kennedy’s term, and use the way he handled them to conclude that he was a president who did everything he could to avoid all-out war, whether of the nuclear variety (over the construction of the Berlin Wall or the installation of Russian missiles in Cuba) or something less apocalyptic (the decision to abandon the anti-Castro forces at the Bay of Pigs, and an early reluctance to commit significant ground forces in Indochina).

Add to this some comments contemplating withdrawal from Vietnam that Kennedy made not long before his assassination, and a case begins to come into focus. But begin is all it does. Most of the rest of the film is devoted to images of an embattled President Johnson and brief glimpses of the Vietnam war itself: nothing new, in other words. The movie’s point, it’s claimed, is the hardly novel idea that it really does matter who is president. President Kennedy might well have called a halt in Vietnam; President Johnson didn’t.

But that’s not really what “Virtual JFK” is about. The movie’s real target finally emerges emerges in its closing moments when the following quotation appears on-screen: “Every time history repeats itself, the price of the lesson goes up.” Ah, so that’s it. This film is not about Vietnam — not really. It’s about Iraq, and Kennedy’s role in it is to act as El Cid, a “virtual JFK” in a very different sense, sent forth to do battle with those wicked Republicans one more time. Thus we see Kennedy in press c onference after press conference, his deftness, charm, and eloquence a devastating rebuke both to the sourpuss, crudely belligerent, Grand Old Party he occasionally finds time to tease and also, by implication, to the current occupant of the White House — tongue-tied, bellicose and, as president, responsible for a war that need not have been.

If you think some of that sounds like caricature as much as history (actual or virtual), you’re right.

Through September 30 (209 W. Houston St., between Sixth Avenue and Varick Street, 212-727-8110).