Most likely not, at least not to the extent that the article is claiming.
Timeline.com's claim: As was said in the question, the linked article references a '1942 government decree', and further on in the article the author states "March 27, 1942, was the day the first train of Jews left Paris for Auschwitz, and also the day of the barbershop decree." March 27, 1942, was indeed the first deportation of Jews from Paris to Auschwitz, however I have been unable to find any information regarding 'government decrees' happening on that day.
If the author either read the decree itself or read a notable source that mentioned it, they would have no reason to not either be more specific about what it was called or add a link to their source. This, coupled with the fact that historical government records are usually well document, means that source of the claim is likely fabricated entirely or heavily distorted, and thus the claim itself is likely not true.
Possible origin of the 'decree' claim: While searching for the decree source, the only similar reference I found was this libcom.org article from 2006, which seems to be the source of a good amount of text on the original 2007 zazou Wikipedia page. The libcom.org article has the following line:
In fact, after the Government decree of 1942, which authorised the collection of hair from barber-shops to be made into slippers, they grew their hair longer!
This version of the claim is even less specific and even easier to dismiss. If there was a 'Government decree of 1942', i.e. a single decree for the year, it should be very easy to find. Judging by libcom.org's black-and-red iconography it seems like they'd want to paint the zazou's in a very rebellious and anarchist light by saying they defied the government's fascist decrees. Again, since they have no reason to not source their decree claim, it's likely that either they or their source made it up.
Feasibility of human hair slippers and sweaters: A quick and kind of creepy search definitely shows that human hair can be used to make clothing, so human hair could be used to bolster clothing production. Furthermore, clothing rationing certainly happened in several countries during WWII, such as France or Great Britain, so such desperate supplements may have been considered or used.
Therefore, although there's no clear evidence of it being official government policy, it's certainly possible that human hair was used as supplemental clothing material. However, this just makes the claim less believable, not more: if the government decreed that human hair would be collected, why would it only be used for slippers and sweaters? All clothing could benefit from this extra 'free-range wool', there's no apparent reason for its use to be restricted.