We consider a cell-free massive multiple-input multiple-output (CF-mMIMO) system with joint unicast and multi-group multicast transmissions. We derive exact closed-form expressions for the downlink achievable spectral efficiency (SE) of both unicast and multicast users. Based on these expressions, we formulate a joint optimization problem of access point (AP) selection and power control subject to quality of service (QoS) requirements of all unicast and multicast users and per-AP maximum transmit power constraint. The challenging formulated problem is transformed into a tractable form and a novel accelerated projected gradient (APG)-based algorithm is developed to solve the optimization problem. Simulation results show that our joint optimization strategy enhances notably the sum SE (SSE) (up to 58%) compared to baseline schemes, while maintaining low complexity.