When preparing to make a French jacket it is important to think not only about a fashion fabric (tweeds, plaids or buckles) but lining as well. And this could be quite challenging. You have to think ahead about the whole project.
Very often I use Viscose as a lining to my garments. It is thin and light and it is easy to work with. It is as well not so expensive.
“Viscose is a solution of cellulose xanthate made by treating a cellulose compound with sodium hydroxide and carbon disulfide. Byproducts include sodium thiocarbonate, sodium carbonate, and sodium sulfide. The viscose solution is used to spin the fiber viscose rayon, or rayon, a soft man-made fiber commonly used in dresses, linings, shirts, shorts, coats, jackets, and other outer wear. It is also used in industrial yarns (tyre cord), upholstery and carpets.” (quoted from Wikipedia)