If a neighbour's tree overhangs our property and sheds leaves in the garden and in the swimming pool, are we permitted to cut the offending branches off, and return them to the neighbour?

Sections 1347 and 1348 of the Civil code probably apply

Section 1347. The owner of a piece of land may cut off and keep roots of a tree or bush which have penetrated from the adjoining piece of land. He may also cut off and keep overhanging branches after giving the possessor of the adjoining piece of land reasonable notice to remove them, such notice not having been complied with.

Section 1348. Fruits falling naturally upon adjoining land are presumed to be fruits of such land.

Why not ask the neighbour first... ? If they are Thai, and you don't speak Thai, perhaps ask some who does to ask them first...

I would say dumping them, if you do get permission on their side, would probably not be too neighbourly .... dispose of yourself!

Being a good neighbour works both ways!.... You'll probably need to do it again, within a year or less.... so don't p' them off!