This paper proposes a user-centric split federated learning (UCSFL) framework for user-centric cell-free multiple-input multiple-output (CF-MIMO) networks to support split federated learning (SFL). In the proposed UCSFL framework, users deploy split sub-models locally, while complete models are maintained and updated at access point (AP)-side distributed processing units (DPUs), followed by a two-level aggregation procedure across DPUs and the central processing unit (CPU). Under standard machine learning (ML) assumptions, we provide a theoretical convergence analysis for UCSFL, which reveals that the AP-cluster size is a key factor influencing model training accuracy. Motivated by this result, we introduce a new performance metric, termed the latency-to-accuracy ratio, defined as the ratio of a user's per-iteration training latency to the weighted size of its AP cluster. Based on this metric, we formulate a joint optimization problem to minimize the maximum latency-to-accuracy ratio by jointly optimizing uplink power control, downlink beamforming, model splitting, and AP clustering. The resulting problem is decomposed into two sub-problems operating on different time scales, for which dedicated algorithms are developed to handle the short-term and long-term optimizations, respectively. Simulation results verify the convergence of the proposed algorithms and demonstrate that UCSFL effectively reduces the latency-to-accuracy ratio of the VGG16 model compared with baseline schemes. Moreover, the proposed framework adaptively adjusts splitting and clustering strategies in response to varying communication and computation resources. An MNIST-based handwritten digit classification example further shows that UCSFL significantly accelerates the convergence of the VGG16 model.