Connectivity and conductivity of two-dimensional fracture networks (FNs), as an important type of continuous random networks, are examined systematically through Monte Carlo simulations under a variety of conditions, including different power law distributions of the fracture lengths and domain sizes. The simulation results are analyzed using analogies of the percolation theory for discrete random networks. With a characteristic length scale and conductivity scale introduced, we show that the connectivity and conductivity of FNs can be well described by universal scaling solutions. These solutions shed light on previous observations of scale-dependent FN behavior and provide a powerful method for quantifying effective bulk properties of continuous random networks.