Fine-grained entity typing (FGET) aims to classify named entity mentions into fine-grained entity types, which is meaningful for entity-related NLP tasks. For FGET, a key challenge is the low-resource problem — the complex entity type hierarchy makes it difficult to manually label data. Especially for those languages other than English, human-labeled data is extremely scarce. In this paper, we propose a cross-lingual contrastive learning framework to learn FGET models for low-resource languages. Specifically, we use multi-lingual pre-trained language models (PLMs) as the backbone to transfer the typing knowledge from high-resource languages (such as English) to low-resource languages (such as Chinese). Furthermore, we introduce entity-pair-oriented heuristic rules as well as machine translation to obtain cross-lingual distantly-supervised data, and apply cross-lingual contrastive learning on the distantly-supervised data to enhance the backbone PLMs. Experimental results show that by applying our framework, we can easily learn effective FGET models for low-resource languages, even without any language-specific human-labeled data. Our code is also available at https://github.com/thunlp/CrossET.