Gas is used in displacing oil for enhanced oil recovery because of its high microscopic-displacement efficiency. However, the process at the reservoir scale suffers from poor sweep efficiency due to density and viscosity differences compared to in-situ fluids. Foam substantially increases the viscosity of injected gas and hence improves the sweep. Foam rheology in 3D geological porous media has been characterized both theoretically and experimentally. In contrast, the knowledge of foam flow in fractured porous media is far less complete. A companion paper (AlQuaimi and Rossen, 2017c), We focused on foam generation and propagation in a fully characterized model fracture. Here we focus on foam rheology in the same model fracture. This investigation is conducted by varying superficial velocities of gas and surfactant solution. We find in this model fracture the same two foam-flow regimes central to the understanding of foam in 3D porous media: a low-quality regime where pressure gradient is independent of liquid velocity and a high-quality regime where pressure gradient is independent of gas velocity. The transition between regimes is less abrupt than in 3D porous media. Our study directly relates flow regime to foam texture through observation of bubble size, bubble trapping and mobilization, and foam stability as functions of superficial velocities which allows comparison with our understanding of the mechanisms behind the two flow regimes in 3D porous media. Additionally, foam is shear-thinning in both regimes. However, the mechanisms thought to be behind the two flow regimes in 3D porous media do not appear in our model fracture. Foam is not at the limit of stability in the high-quality regime. Mobility in the high-quality regime, instead, reflects reduced and fluctuating foam generation at high foam quality. Moreover, bubble size is not fixed at approximately pore size, the mechanism thought to control the low-quality regime in 3D porous media. Instead, bubbles are much smaller than pores. Finally, for this model fracture, the investigation of vertical flow reaches the same findings as for horizontal flow, with somewhat lower pressure gradient.