For a bit more detail, you should know that vertex colours are 'multiplied' with the texture colours, by default.
This means that if either colour is black, the result will be black; if one colour is pure red and one is the other is pure blue, the result is still black; if one colour is white, the result is the other colour.
I have made a few very basic shaders for simple use with SFML that you can try out. They are here:
https://github.com/Hapaxia/Lens/tree/master/LensFirst one to try is
standard.frag.
This does the same multiplication with the two colours but allows you specify an "amount" ratio. This is just the mix between the two. e.g. 0 is texture colour, 1 is vertex colour multiplied in, 0.5 is half way between the two.
If that isn't what you want, you should maybe try
blend.frag and
blendColor.frag.
These do not multiply the two colours together. Instead, the "amount" ratio is just the 'mix' between the two colours. This can be useful for 'tinting' textures. e.g. 0 is texture colour, 1 is vertex colour, 0.5 is half of each.
and example would be if the texture colour is red and the vertex colour is blue, with an "amount" of 0.5, it would be a purple (0.5 red + 0.5 blue).
blendColor is only different from blend is that it ignores the alpha of the vertex colour.
If that still doesn't do what you want, you could try
adjustments.frag.
This allows you to perform some standard image colour manipulations: gamma, de-saturation, inversion, contrast and brightness. Note that this shader completely ignores vertex colours.
In conclusion, I think blend or blendColor may be what you're looking for but it would depend on your exact requirements.
Also, these shaders are based on the basic SFML shader ideas so you can just use the fragment shader alone without a custom vertex shader and it should work immediately!