In contemporary data center networks (DCNs), scheduling groups of parallel flows (coflows) has emerged as a critical task for improving application-level communication efficiency. Recently, research interest has shifted to hybrid-switched DCN architectures that integrate optical circuit switches (OCSs) and electrical packet switches (EPSs) to respectively manage both high-volume and low-volume traffic efficiently. To minimize the overall communication latency, it is essential to effectively coordinate coflows over hybrid network links. The complexity of this task, however, is substantially greater than that of scheduling on monolithic network links of either OCS or EPS. The complexity arises from allocating flows between OCS and EPS in a coordinated way, while considering both the reconfiguration delay of circuit switching in OCS and the bandwidth limitation of packet switching in EPS, and completing the transmission in the shortest time. The current solutions for scheduling coflows in hybrid-switched DCNs are primarily based on heuristics and lack formal performance guarantees. In this paper, we first establish a coflow scheduling framework for hybrid-switched DCNs, which can transform any given circuit schedule (denoted as SC) designed for pure OCS into a corresponding hybrid scheduling scheme SH. On this basis, we further present two approximation algorithms w.r.t SC under two primary reconfiguration models (i.e., all-stop model and not-all-stop model) of OCS to minimize the coflow completion time (CCT) in a hybrid-switched DCN. Theoretical analysis demonstrates that our algorithms can achieve the optimal traffic partitioning for hybrid switch environments w.r.t SC. Furthermore, we theoretically prove that the proposed algorithms can transform any SC for pure OCS with an approximation rate of λ into a corresponding coflow scheduling scheme SH tailored for hybrid switches with the approximation rate of λ+1. Extensive simulations utilizing Facebook data traces show that our algorithm performs well in minimizing the CCT compared to state-of-the-art schemes.