Conversational recommender systems (CRS) have shown great success in accurately capturing a user's current and detailed preference through the multi-round interaction cycle while effectively guiding users to a more personalized recommendation. Perhaps surprisingly, conversational recommender systems can be plagued by popularity bias, much like traditional recommender systems. In this paper, we systematically study the problem of popularity bias in CRSs. We demonstrate the existence of popularity bias in existing state-of-the-art CRSs from an exposure rate, a success rate, and a conversational utility perspective, and propose a suite of popularity bias metrics designed specifically for the CRS setting. We then introduce a debiasing framework with three unique features: (i) Popularity-Aware Focused Learning, to reduce the popularity-distorting impact on preference prediction; (ii) Cold-Start Item Embedding Reconstruction via Attribute Mapping, to improve the modeling of cold-start items; and (iii) Dual-Policy Learning, to better guide the CRS when dealing with either popular or unpopular items. Through extensive experiments on two frequently used CRS datasets, we find the proposed model-agnostic debiasing framework not only mitigates the popularity bias in state-of-the-art CRSs but also improves the overall recommendation performance.