The mobile network's Read&Go runs on a touch-screen A5-sized device that has a 3G mobile chip and WiFi to refresh the news, even while the reader is travelling.
It uses ePaper and eInk technology that reportedly makes it, as much as possible, like reading a traditional newspaper.
Display technology ensures it is readable in bright sunlight, unlike a laptop.
It is reportedly similar in design to Amazon's Kindle electronic book but without the keyboard.
Five French newspapers are taking part in the trial, including L'Equipe, Le Monde, Les Echos, Le Parisien and Telerama.
The device has 1Gb storage, which is enough space for 200 newspapers, and comes pre-loaded with 30 ebooks, including city guides and novels.
Around 150 readers will trial it over two months, testing how well the technology works and how easy it is to use.
If successful, the e-newspaper could reinvigorate the newspaper market and allow for more innovative interactive advertising, which would provide a more promising outlook for print.