What are farmers (in Israel) supposed to do with all their free time during the shemita year? Are we, today, supposed to do anything special during the shemita year (in addition to actions related to produce of the land). I am asking about actions we might take that are reflective of what farmers in the past did (or might have done) with their extra time?
As has already been mentioned in the comments - with their now free time, it affords the farmers the opportunity to learn and daven more.
Rav Tzadok in the first Pri Tzadik of Behar writes:
מפני שמצות שמיטה היא כמו מצות שבת שהוא קבלת מלכות שמים ששובתין כל אומה ישראלית ביום השבת וכן שמיטה בא"י שהי' כל עסקיהם בעבדות הארץ, ובשמיטה פנוים לתורה ועבודה,
...Because the mitzvah of Shemitta is like the mitzvah of Shabbos, that is an acceptance of the kingship of Heaven - that every Jew stops on the day of Shabbos, and similarly during Shemitta in Eretz Yisroel; all those that engage in working the land - during shemittah they turn to Torah and prayer.