We propose FluoGAN, an unsupervised hybrid approach combining the physical modelling of fluorescence microscopy timelapse acquisitions with a Generative Adversarial Network (GAN) for the problem of image deconvolution. Differently from standard approaches combining a least-square data fitting term based on one (longtime exposure) image with sparsity-promoting regularisation terms, FluoGAN relies on a data fitting term defined as a distribution distance between the fluctuating observed timelapse (short-time exposure images) and the generative model. The distance between these two distributions is computed using adversarial training of two competing architectures: a physics-inspired generator simulating the fluctuation behaviour as a Poisson process of the observed images combined with blur and undersampling, and a standard convolutional discriminator. FluoGAN is a fully unsupervised approach requiring only a fluctuating sequence of blurred, undersampled and noisy images of the sample of interest as input and it can be complemented with prior knowledge on the desired solution such as sparsity, non-negativity etc. After having described in depth the main ideas behind FluoGAN, we formulate the corresponding optimisation problem and report several results on a simulated and real phantoms used by microscopy engineers to quantitatively assess spatial resolution. The comparison of FluoGAN with state-of-the-art methodologies shows improved resolution and allows for high-precision reconstruction of very fine structures in challenging real Ostreopsis cf Ovata data.