Developing channel-adaptive deep joint source-channel coding (JSCC) systems is a critical challenge in wireless image transmission. While recent advancements have been made, most existing approaches are designed for static channel environments, limiting their ability to capture the dynamics of channel environments. As a result, their performance may degrade significantly in practical systems. In this paper, we consider time-varying block fading channels, where the transmission of a single image can experience multiple fading events. We propose a novel coarse-to-fine channel-adaptive JSCC framework (CFA-JSCC) that is designed to handle both significant fluctuations and rapid changes in wireless channels. Specifically, in the coarse-grained phase, CFA-JSCC utilizes the average signal-to-noise ratio (SNR) to adjust the encoding strategy, providing a preliminary adaptation to the prevailing channel conditions. Subsequently, in the fine-grained phase, CFA-JSCC leverages instantaneous SNR to dynamically refine the encoding strategy. This refinement is achieved by re-encoding the remaining channel symbols whenever the channel conditions change. Additionally, to reduce the overhead for SNR feedback, we utilize a limited set of channel quality indicators (CQIs) to represent the channel SNR and further propose a reinforcement learning (RL)-based CQI selection strategy to learn this mapping. This strategy incorporates a novel reward shaping scheme that provides intermediate rewards to facilitate the training process. Experimental results demonstrate that our CFA-JSCC provides enhanced flexibility in capturing channel variations and improved robustness in time-varying channel environments.