As machine learning is increasingly applied in an online fashion to deal with evolving data streams, the fairness of these algorithms is a matter of growing ethical and legal concern. In many use cases, class imbalance in the data also needs to be dealt with to ensure predictive performance. Current fairness-aware stream learners typically attempt to solve these issues through in- or post-processing by focusing on optimizing one specific discrimination metric, addressing class imbalance in a separate processing step. While C-SMOTE is a highly effective model-agnostic pre-processing approach to mitigate class imbalance, as a side effect of this method, algorithmic bias is often introduced. Therefore, we propose CFSMOTE - a fairness-aware, continuous SMOTE variant - as a pre-processing approach to simultaneously address the class imbalance and fairness concerns by employing situation testing and balancing fairness-relevant groups during oversampling. Unlike other fairness-aware stream learners, CFSMOTE is not optimizing for only one specific fairness metric, therefore avoiding potentially problematic trade-offs. Our experiments show significant improvement on several common group fairness metrics in comparison to vanilla C-SMOTE while maintaining competitive performance, also in comparison to other fairness-aware algorithms.