If the tree is on the road reserve and Council is the responsible authority (that is VicRoads is not the responsible authority which would be the case if is an arterial road) and the road is on Councils Road Register then council is required to attend to trees.
Regards damage to fencing if damage was caused by tree on road reserve then council would be liable.
If the tree is not in road reserve that is on land owned by others then it is the owners responsibility.
See extract from Road Management Act 2004 Code Of Practice.
Matthew McIntyre Development Engineer Golden Plains Shire Council P: 03 5220 7119 | M: Golden Plains Shire Council | F: 03 5220 7100 E: email@example.com | W: goldenplains.vic.gov.au
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