Move your illustration layer below the texture, if it isn’t already, and set the blend mode of your texture to Soft Light.
Adjust opacity settings until you achieve a nice balance between texture and colour.
You don’t want your texture to look too overpowering as it can make the illustration less appealing – less is more.
Apply a Levels adjustment layer on top of your texture and boost contrast. Levels bring out the detail of the texture and it also gives a more grainy look which adds a nice aesthetic.
Clip this Levels layer to the texture layer so that you can edit it later on once you have overlaid it on the illustration.