Here's a brown background pattern with subtle stripes. I hope you'll like the color. If not, feel free to change it using an image editor, if you know how of course. Personally, I'm using GIMP to create these backgrounds.
Source V. Hartikainen
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A seamless pattern formed from a sports car on clker.com. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
Abstract Arbitrary Geometric Background derived from an image on Pixabay.
Source GDJ
More tactile goodness. This time in the form of some rough cloth.
Source Bartosz Kaszubowski
A background pattern with wavy green vertical stripes. This one has green stripes on a white background. Download if you like it.
Source V. Hartikainen
Classic 45-degree pattern, light version.
Source Luke McDonald
Seamless pattern formed from a tile that can be had by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Formed from a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Dark, square, clean and tidy. What more can you ask for?
Source Jaromír Kavan
Prismatic Curved Diamond Pattern 2 No Background
Source GDJ
A seamless pattern of "sewn stripes" colored in light gray.
Source V. Hartikainen
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
From a drawing in 'Uit de geschiedenis der Heilige Stede te Amsterdam', Yohannes Sterck, 1898.
Source Firkin
Free tiled background with colorful stripes and white splatter.
Source V. Hartikainen
Zero CC tileable ground cracked, crackled, texture, made by me.
Source Sojan Janso
Seamless pattern formed from a tile that can be extracted by selecting the rectangle in Inkscape and using shift-alt-i.
Source Firkin
Prismatic Curved Diamond Pattern No Background
Source GDJ