Hyperspectral imaging has become a significant source of valuable data for astronomers over the past decades. Current instrumental and observing time constraints allow direct acquisition of multispectral images, with high spatial but low spectral resolution, and hyperspectral images, with low spatial but high spectral resolution. To enhance scientific interpretation of the data, we propose a data fusion method which combines the benefits of each image to recover a high spatio-spectral resolution datacube. The proposed inverse problem accounts for the specificities of astronomical instruments, such as spectrally variant blurs. We provide a fast implementation by solving the problem in the frequency domain and in a low-dimensional subspace to efficiently handle the convolution operators as well as the high dimensionality of the data. We conduct experiments on a realistic synthetic dataset of simulated observation of the upcoming James Webb Space Telescope, and we show that our fusion algorithm outperforms state-of-the-art methods commonly used in remote sensing for Earth observation.