There are several examples where OUTPUT pin set to HIGH/LOW state after waking from sleep (e.g. Waking from sleep with a timer, Powering off external devices, etc.). In these sketches, OUTPUT pin mode is changed to INPUT before going back to sleep again. Why?
As tested in Configuring pins as inputs/outputs section, overall current consumption should be the same if pin is in OUTPUT LOW or in INPUT mode state. I could think of some safety reason for this, if a voltage is accidentally connected to OUTPUT LOW pin, it could cause troubles. Is this the case?
Whether you set pins to output, and high or low, or to input pullup or indeed input, when going to sleep, depends on what devices or components you actually have connected.
There is no universal optimum method that I am aware of.
The twist in this particular example, is that AFAIK, DS1307 doesn't need any supply voltage to be able to communicate via I2C (if battery is inserted of course).
Pins which are allowed to float can cause excess power consumption in sleep mode.
For a project with I2C devices, it should be enough to call Wire.end() then set all pins as required for minimum power consumption before entering sleep mode. On waking, undo it all in the reverse order th call Wire.begin().
As recommended above, test carefully.