Contact tracing (CT) apps have been rolled out as part of combined efforts to control the COVID-19 pandemic. However, these apps haven't been download by the totality of the population, with users raising concerns over the usage of data and data protection. This article analyzes how different app providers and data protection levels can affect the willingness to download a COVID-19 contact tracing app between university students, and if there is a difference between students who downloaded and didn't download the app. Through the usage of a factorial survey experiment (FSE) the paper statistically analyses the data protection and trust (DPT) requirements, using the French COVID-19 CT as a use case. The results show that universities have a positive impact on the trust levels of app providers, while private companies tend to have a negative impact on trust. Subjects also have high expectations on data protection. Our results highlight the importance of data protection and app providers for building trust with users of CT COVID-19 apps.