Salut Jack,

"where the shade of the tall broad-leaf trees creates a cosy shelter from the outside. There, I can recharge my batteries before venturing once more into the world."

In the context of the extract above, the sense is of being rejuvenated (one's batteries being recharged) the meaning in English is not literal just a term used to explain or express the beneficial effect on the psyche.

However, using the term "pile" does not lend itself in this way. The meaning would be understood to refer to a dry cell (rechargeable or not) as used in a watch or some other type of equipment.

This is my understanding  --  hope it helps

Bonne journée

Jim