"Coquelicot" is French for "poppy", and is, indeed a bright orangey-red.

All I can say about its fashionableness is that the dyes for red cloth, especially rose madder , were occasionally in short supply, because, of course, they were used for uniforms, and also because English dyers were cut off from the source. Rose madder, although occasionally growing wild in England, has traditionally been a French product. So it may be that the use of "coquelicot" is saying something abotu Isabella's patriotism,I don't know.

The other reference to Coquelicot that comes up is the supposed portrait of JA in JAmes Stanier Clarke's book, which had coquelicot trim on the dress, IIRC.