A cell-free massive multiple-input multiple-output (CF-mMIMO) system is considered for enhancing the monitoring performance of wireless surveillance, where a large number of distributed multi-antenna aided legitimate monitoring nodes (MNs) proactively monitor multiple distributed untrusted communication links. We consider two types of MNs whose task is to either observe the untrusted transmitters or jam the untrusted receivers. We first analyze the performance of CF-mMIMO surveillance relying on both maximum ratio (MR) and partial zero-forcing (PZF) combining schemes and derive closed-form expressions for the monitoring success probability (MSP) of the MNs. We then propose a joint optimization technique that designs the MN mode assignment, power control, and MN-weighting coefficient control to enhance the MSP based on the long-term statistical channel state information knowledge. This challenging problem is effectively transformed into tractable forms and efficient algorithms are proposed for solving them. Numerical results show that our proposed CF-mMIMO surveillance system considerably improves the monitoring performance with respect to a full-duplex co-located massive MIMO proactive monitoring system. More particularly, when the untrusted pairs are distributed over a wide area and use the MR combining, the proposed solution provides nearly a thirty-fold improvement in the minimum MSP over the co-located massive MIMO baseline, and forty-fold improvement, when the PZF combining is employed.