Detecting hot social events (e.g., political scandal, momentous meetings, natural hazards, etc.) from social messages is crucial as it highlights significant happenings to help people understand the real world. On account of the streaming nature of social messages, incremental social event detection models in acquiring, preserving, and updating messages over time have attracted great attention. However, the challenge is that the existing event detection methods towards streaming social messages are generally confronted with ambiguous events features, dispersive text contents, and multiple languages, and hence result in low accuracy and generalization ability. In this paper, we present a novel reinForced, incremental and cross-lingual social Event detection architecture, namely FinEvent, from streaming social messages. Concretely, we first model social messages into heterogeneous graphs integrating both rich meta-semantics and diverse meta-relations, and convert them to weighted multi-relational message graphs. Second, we propose a new reinforced weighted multi-relational graph neural network framework by using a Multi-agent Reinforcement Learning algorithm to select optimal aggregation thresholds across different relations/edges to learn social message embeddings. To solve the long-tail problem in social event detection, a balanced sampling strategy guided Contrastive Learning mechanism is designed for incremental social message representation learning. Third, a new Deep Reinforcement Learning guided density-based spatial clustering model is designed to select the optimal minimum number of samples required to form a cluster and optimal minimum distance between two clusters in social event detection tasks. Finally, we implement incremental social message representation learning based on knowledge preservation on the graph neural network and achieve the transferring cross-lingual social event detection. We conduct extensive experiments to evaluate the FinEvent on Twitter streams, demonstrating a significant and consistent improvement in model quality with 14%-118%, 8%-170%, and 2%-21% increases in performance on offline, online, and cross-lingual social event detection tasks.