Concrete ML and TFHE-rs are Zama libraries for fully homomorphic encryption (FHE). Concrete ML is a toolkit for privacy-preserving machine learning with scikit-learn-like models and can convert PyTorch and ONNX models to FHE, so that predictions can run on encrypted inputs. They are meant for developers and data specialists who want to process sensitive data without decrypting it, and offer a European building block next to cloud services where the provider sees the plaintext. They run on your own infrastructure.
Zama SAS is a French company headquartered in Paris. The source code is on GitHub under the BSD-3-Clause-Clear licence, but according to the project's FAQ this use covers only development, research, prototyping and experimentation. Commercial use requires a patent licence from Zama, so unrestricted commercial use is not covered by the open licence. No foreign parent company has been established. Because they are libraries that you run yourself, the data stays with you; a processor relationship with Zama does not arise automatically.