The local council could not finance the project as planned.

In the sentence 'The local council could not finance the project as planned', the word 'finance' follows the modal 'could not' and takes 'the project' as its object. This shows that 'finance' is being used as the main verb of the sentence, meaning 'to provide funding for'. While 'finance' can be a noun in other contexts, here it clearly functions as a verb. Therefore, the correct word class is verb.