Your question hints at two separate questions, which I can hopefully address in sequence. The first relates to the term "bliaud" (or bliaut, or one of a number of different, related spellings)--when was it used, and what does it mean? The second relates to the cut of the garment we have generally come to call a bliaud or bliaut based on how the garment is described in literature compared to the sources we have, which are generally sculptural or pictorial (as there are no extant garments that meet these descriptions)--that is, when do we stop seeing the characteristic shape with dangling sleeves, tight fitting through the body, and fairly generous, often trailing, skirts for women.

So, to answer the first, an old standby text, Eunice Goddard's Women’s Costume in French Texts of the Eleventh and Twelfth Centuries ( Johns Hopkins University 1927) provides numerous examples of the word used in French lais and romances of the 12th and early 13th centuries. For example, the passage below talks about the tightness of the bliaut, its fur trim, and use of gold:

li blials qu'ele ot vestu,
Moult estoit ciers et bien ovrés,
D'une ermine fu tos forrés.
Plus de v. onces d'or, sans faille
Avoit entor le kieueçaille ;
As puins en ot plus de iiii onces ;
Par tot avoit asis jagonsses,
Et autres pieres de vertu
Qui furent deseur l'or batu.

Nicole Smith, in Sartorial Strategies, quotes Marie de France's descriptions of clothing in Lanval, also specifying fur, luxurious colours, and side lacing that reveals the shift beneath. Tight lacing is often used in the lais and romances to signify high status and virtue.
There is good evidence in some of the texts that "bliaut" (and its cognates in other European languates) was originally a term referring to a type of fabric, widely thought to be fine silk based on the fact that these garments were clearly luxury items (with their gold and fur trimmings) and on the way the fabric is draped in many pictorial and sculptural depictions. For example, in Middle High German, we have a garment made of "bliat" :

Si hiez ein bette dar ze hant
Rilich und schone machen
Kulter und lilachen
Purper und bliat
Küneklicher bettewat

The term then is used substantively to refer to a garment of such cloth. Incidentally, far from the idea that "bliauts" were exclusively French, there are references to garments or fabric using clearly related words in Middle High German, Italian, Provencal, Spanish, Norman French, and Middle English.

So based on this, we know a bliaut is a high-status garment made of costly fabric, often with trim of fur or gold, and often laced tightly. But what can this tell us about the actual cut and evolution of such garments? Not a lot, besides the tight lacing--which appears to become a trope in the literature (according to Nicole Smith) and the fact they were made of costly materials.

This is where looking at the pictorial and sculptural evidence. Costume historians, based on this evidence (particularly some of the sculptures at Chartres Cathedral), formerly postulated that the bliaut was an extreme fashion only in existence for maybe 30 years in the mid-12th century (approx. 1140-1170 or so. Based on looking at these statues, all kinds of theories were formulated around construction, including the use of an exterior corset or bias cutting to get the fabric to "flow" the way it does on the sculptures. However, it can be clearly demonstrated that what we call a "bliaut" evolves from earlier styles (such as can be seen on the Bayeaux tapestry) and then evolves into later styles. The sleeves, in particular, seem to be a fashion that exists as early as the late 11th century, although the gowns at that point are not as tight. Note that most of these sleeves have tight upper arms and then widen at the lower arm, and there are different shapes--some triangular and some scoop shape, with the start of the widening often happening at about the middle of the forearm (these are generally not batwing sleeves or sleeves that widen through the entire length of the arm, as will be seen later in houppelande sleeves).

So when the transition to the tighter sleeves and looser-fitting gowns seen by the the 1220s or 1230s for both men and women of high status? One of the few pieces I know of from this period is the tomb effigy of Eleanor of Aquitaine at Fontevraud Abbey. She died in 1204, and she is clearly portrayed in a gown with tighter sleeves and a generous cut. It's not known precisely when the tomb effigy was sculpted (the V&A, which has a plaster copy, dates it between 1204 and 1210). Henry II died about 15 years earlier, and his effigy seems to show a transitional stage of sleeve types--his sleeves show a wider oversleeve (dropping down maybe 3x the width of his hand) over a tighter undersleeve. So it looks like this might be the key period to look for the transition, at least in England and France, away from the long, pendant sleeves. (The pendant sleeves seem to survive elsewhere, such as in Italy, into the early 13th century). Note that it is absolutely possible that the term "bliaut" survived on to refer to a high-status garment made of costly fabric and trimmed in fur well past this period--just as our word "gown" might refer to a high-fashion garment in many different periods with many different cuts, particularly because the term seems to have come from a term for a type of costly fabric.

As far as cut, no great deviation from techniques of patterning and cut found in extant garments from the 11th, 12th, and 13th centuries is required to get the "look" of the classic bliauts of Chartres Cathedral or elsewhere. It's thought that the distinctive look of "pleating" on these garments may simply be a way of depicting the look of fine fabric side laced tightly through the torso.