If it is built on the property line then the cost should be agreed upon and shared. If you are doing a more expensive fence you could offer to make up the difference.
Without any costs being covered you would simple build the fence on your side of the property line.
Always best to keep an open mind and to foster good relations with the neighbour. To that end, I think it's better to meet them first and then bring it up over the course of conversation.
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