This was the school of literature that Aristotle Valaoritis belonged to as well as Ioannis Zampelios who are very famous Lefkádian poets. Andreas Kalvos and Dionysios Solomos are in there too. The articles written about this school will tend to focus on people known to that locality ie you come across ones written from the view of a person from Zakynthos as Dionysios Solomos was from there and this one is written from the perspective of a Lefkadian since that’s where I am. Hence I mentioned Valaoritis first where usually you would see a note about pre Solomos, Solomos, and post Solomos poets.
The Heptanese school is characterised by a love of nature, freedom and homeland with reference to the role that religion played in their lives. It was also folkloreish in content and often romantized life in a way only poetry can taking inspiration from Italy. They were written in Dimotiki or Demotic as apposed to Katharevousa which is to say its written in the common Greek that was spoken as opposed to the posher, purist form which was a simplication of Ancient Greek that was used for formal, business occasions.
As I have already written ample amounts about the Lefkadian poets and I have never been to Zakynthos I can’t tell you much more as that’s the real centre of this particular movement.
For information on the other schools of thought see here