Usually when you compute the diffraction pattern of two slits of finite width, you consider the aperture to be the convolution of two infinitesimal slits, and a finite aperture. Now as you may know, the Fraunhofer diffraction pattern is the Fourier transform of the aperture function. The convolution theorem tells us that the Fourier transform of a convolution of two functions is the product of the Fourier transforms of the individual functions.
What that means is that if you consider the centers of the slits to be a distance $a$ apart, and they each have a width $w$, then the diffraction pattern will be the product of the pattern you expect from two infinitesimal slits that are distance $a$ apart, and the diffraction pattern of a single aperture of width $w$.
This will look like a cosine function (spacing determined by $a$) whose amplitude is modulated by a sinc function (shape determined by $w$).
See for example this question.