The story...

[Afghan President Hamid] Karzai also worked for the oil company UNOCAL as mentioned by the French paper Le Monde: "...After Kabul and India, where he has studied law, he completed his learnings in the USA, where he acted, for a while, as a consultant for the American oil company Unocal, at the time it was considering building a pipeline in Afghanistan."
http://www.jihadunspun.com/IslamUnderAttack/articles/pohk01.html

Our take...

This quote is based on a translation of the Le Monde article, so let's start by checking it for accuracy. Dave Kopel has this:

The actual sentence was "Après Kaboul et l'Inde ou il a étudié le droit, il a parfait sa formation aux Etats-Unis ou il fut un moment consultant de l'enterprise pétrolière américaine Unocal, quand celle-ci étudiant la construction d'un oléduc en Afghanistan." Translated: After Kabul and India where he had studied law, he completed his training in the United States where he was briefly (literally: "for a moment") a consultant for the American petroleum business Unocal, when it was studying the construction of a pipeline in Afghanistan."
http://www.davekopel.com/Terror/Fiftysix-Deceits-in-Fahrenheit-911.htm

So being a consultant "for a while" shifts to arguably "for a moment" in the original text, but at least there's a qualification there (many sites just say "he worked for Unocal" without clarifying that it was maybe only for a very short period of time).

We shouldn't stop looking here, though, because the Le Monde article doesn't actually have any references for its claim. Let's try to verify it by looking at Karzai's biography, then. The article says he went to Kabul, then India, then the US where he briefly worked for Unocal. How does this match up with what we can read elsewhere?

In 1979, while Karzai was a student in India, the Soviet Union invaded Afghanistan. Karzai’s family fled to Quetta, Pakistan; most of his siblings soon emigrated to the United States, where they established a chain of Afghan restaurants. Karzai chose to join the guerrilla movement to liberate Afghanistan from Soviet military occupation. Although he was not on the front lines, Karzai was a key planner and strategist and, from his base in Pakistan, helped route supplies to the anti-Soviet Islamic guerrillas called mujahideen.

In 1992 Karzai was appointed deputy foreign minister in the administration of Afghan president Burhanuddin Rabbani. Political infighting led Karzai to resign from the post. Meanwhile, the country was beset by civil war as certain mujahideen factions and warlords fought against the new government. In 1996 the Taliban dislodged the Rabbani government in Kābul, reestablishing Pashtun dominance and imposing a fundamentalist regime in most of the country. Karzai briefly aligned himself with the Taliban, but as a moderate Muslim and advocate of women’s rights, he soon became alarmed by the Taliban’s authoritarian policies based on its interpretation of Islam. Karzai returned to Quetta in 1997, joining his father and younger brother in opposition to the Taliban...
http://encarta.msn.com/encyclopedia_701610397/Hamid_Karzai.html

From the article we might assume he'd gone off to the US soon after India, but there's no mention of this here. It's conceivable he might have had contact with Americans, but working for Unocal seems unlikely. Especially as the Russians were in Afghanistan in 1983, would still be there for another six years, and Unocal wouldn't be talking about Afghan pipelines for another 10 years at least.

We could just say that the original Le Monde article was poorly written, perhaps, and he actually worked for them much later. The opportunities seem slim, though. Taliban representatives visited the US to discuss the pipeline in 1997, for instance, but it appears Karzai had become disillusioned with them the year before, so he was hardly a likely candidate.

There are other problems with the "Karzai worked for Unocal" story, not least that both Karzai and the company deny it. Here's Unocals Barry Lane in an interview with Jared Israel:

Jared Israel: ...The other thing that is being asserted everywhere is that Hamid Karzai, the current head of the Afghan 'government' once worked for you.

Barry Lane: Yeah. Yeah, well that's probably one of the great urban legends. He never worked for us.

Jared Israel: He didn't work for somebody else who worked for you?

Barry Lane: No. No, not him. He was never a consultant, never an employee. We've exhaustively searched through all our records to try and find out where the hell that came from.
http://emperors-clothes.com/interviews/lane.htm

Several sources, most notably the documentary film Fahrenheit 9/11, have reported that Karzai once worked as a consultant for the oil company Unocal. Spokesmen for both Unocal and Karzai have denied any such relationship.
http://www.globalsecurity.org/military/world/afghanistan/karzai.htm

Let's review what we have, then.

The original story claims that Karzai was "for a moment" a consultant for Unocal. There's no reference or source to explain how they know this.

The timeline as presented in the story doesn't make sense (we've found no reference to him spending time in the US after India, and Unocal wouldn't be interested in the pipeline for another 10+ years anyway).

Both Unocal and Karzai deny the claim. No evidence has ever been forthcoming to prove them wrong. (And why not? If there is evidence, why not bring it forward? Catching Unocal and Karzai in a lie would be a far bigger scoop than the original story).

Our conclusion: the best you can say about this claim is that it's unproven. More details on sources, at least, are required before we'd take it seriously.