How about something on the lines of:
Dear X,
Just to let you know we will shortly be replacing the fencing and associated posts which border on your garden. As we're responsible for its maintenance and upkeep we 'd really appreciate it if you could refrain from attaching any hanging baskets or similar heavy objects on it to avoid any damage to it. We will do our best to ensure that your garden and plants are not damaged while work is in progress. "
However, wouldn't it be better if you could just knock on their door and have a personal word with them? Or arn't they those kind of neighbours?
We have attached some lightweight trellis to a couple of the fence panels we share with our next door neighbour. It's actually his fence, but we we went 50/50% with him when it needed to be replaced, and we organised the tradesman to do it, so I reckon that wasn't too out of order.