Few-Shot Relation Extraction (FSRE), a subtask of Relation Extraction (RE) that utilizes limited training instances, appeals to more researchers in Natural Language Processing (NLP) due to its capability to extract textual information in extremely low-resource scenarios. The primary methodologies employed for FSRE have been fine-tuning or prompt tuning techniques based on Pre-trained Language Models (PLMs). Recently, the emergence of Large Language Models (LLMs) has prompted numerous researchers to explore FSRE through In-Context Learning (ICL). However, there are substantial limitations associated with methods based on either traditional RE models or LLMs. Traditional RE models are hampered by a lack of necessary prior knowledge, while LLMs fall short in their task-specific capabilities for RE. To address these shortcomings, we propose a Dual-System Augmented Relation Extractor (DSARE), which synergistically combines traditional RE models with LLMs. Specifically, DSARE innovatively injects the prior knowledge of LLMs into traditional RE models, and conversely enhances LLMs' task-specific aptitude for RE through relation extraction augmentation. Moreover, an Integrated Prediction module is employed to jointly consider these two respective predictions and derive the final results. Extensive experiments demonstrate the efficacy of our proposed method.