Differentiable rendering is a growing field that is at the heart of many recent advances in solving inverse graphics problems, such as the reconstruction of 3D scenes from 2D images. By making the rendering process differentiable, one can compute gradients of the output image with respect to the different scene parameters efficiently using automatic differentiation. Interested in the potential of such methods for the analysis of fluorescence microscopy images, we introduce deltaMic, a microscopy renderer that can generate a 3D fluorescence microscopy image from a 3D scene in a fully differentiable manner. By convolving the meshes in the scene with the point spread function (PSF) of the microscope, that characterizes the response of its imaging system to a point source, we emulate the 3D image creation process of fluorescence microscopy. This is achieved by computing the Fourier transform (FT) of the mesh and performing the convolution in the Fourier domain. Naive implementation of such mesh FT is however slow, inefficient, and sensitive to numerical precision. We solve these difficulties by providing a memory and computationally efficient fully differentiable GPU implementation of the 3D mesh FT. We demonstrate the potential of our method by reconstructing complex shapes from artificial microscopy images. Eventually, we apply our renderer to real confocal fluorescence microscopy images of embryos to accurately reconstruct the multicellular shapes of these cell aggregates.