Answer: Anouk
The voice is clearly female, but the wording of the narration is kept ambiguous for most of the film. Only at the end do we discover that we have been listening to the memories of Anouk. The final scenes which she narrates include the throwing of (what is left of) Chitza's ashes into the wind, a symbolic gesture from Vianne to show that she is ready to settle down and the return of Roux the following summer on the pretext that the shop door still squeaks and needs fixing. Now that Anouk is no longer roaming from town to town, she has no further need of the companionship of Pantoufle; he hops out of her life, his injured leg fully healed. Josephine takes over control of the café her husband abandoned, renaming it Café Armande. The film closes with a shot of the statue in the town square (Le Comte's grandfather, who was successful in expelling the Huguenots from town and establishing its previously-cherished tranquility) holding a red balloon. Life wins.