One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.
Source Atle Mo
Crossing lines with a subtle emboss effect on a dark background.
Source Stefan Aleksić
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
Prismatic Curved Diamond Pattern No Background
Source GDJ
This seamless pattern consists of a blue grid on a yellow background.
Source V. Hartikainen
Prismatic Groovy Concentric Background 2 No Black
Source GDJ
Remixed from a drawing in 'Hungary. A guide book. By several authors', 1890.
Source Firkin
You just can’t get enough of the fabric patterns, so here is one more for your collection.
Source Krisp Designs
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Colored maple leaves scattered on a surface. This is tileable, so it can be used as a background or wallpaper.
Source Eady
Here I have tried to create something that would look like maple wood. Not sure how well it's turned out, but at least it looks like wood.
Source V. Hartikainen
A seamless pattern formed from background pattern 102
Source Firkin
This background pattern has futuristic look. So, maybe it could be used on websites or blogs dedicated to video games?!
Source V. Hartikainen
Remixed from a drawing in 'A Girl in Ten Thousand', Elizabeth Meade, 1896.
Source Firkin
From a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.
Source Firkin
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A dark brown fabric-like background texture with seamless pattern of winding stripes.
Source V. Hartikainen
Remixed from a drawing in 'Canadian forest industries July-December', 1915
Source Firkin
Can’t believe we don’t have this in the collection already! Slick woven pattern with crisp details.
Source Max Rudberg
Looks a bit like concrete with subtle specks spread around the pattern.
Source Mladjan Antic