Did foreign countries ever ban media produced by Napoleonic France (newpapers, art, books, ect) on the basis that it was 'foreign propaganda'? Could a British individual be able to obtain, say, French newspapers, or would possession of such things be considered problematic or untrustwory?

Absolutely. That was the main goal of the Spanish and Portuguese Inquisitions. Everything that was deemed "unsafe" for public consumption was censored and it was mostly related to French napoleonic propaganda. Spanish and Portuguese artists at the time who were in favor of Napoleon also had a very hard time and spent many days in jail, like Goya, for instance.