thank you. If the contractor placed a board on the road without securing it to the ground in the knowledge that there was a predicted storm or high winds then I cannot see that this amounts to force majeure ( act of God) but rather was negligence on his part as their would be at least a significant risk if not a certainty that such a board would be blown by the wind. naturally, it could not be predicted that it would have blown into your car, but it is reasonably foreseeable that this would have been a risk that it would have damaged vehicles parked nearby in the circumstances
such a claim for negligence in this regard is a claim made under the law of tort. In order to prove a case in tort, you need to be able to show that another person owes you (1) a duty of care which in the case of a contractor working for you, of course you can; (2) that they fell short of that duty of care - we will return to this and (3) that you suffered loss by way of personal injury or property damage as a result which again you can.
This leaves you with (2) as the remaining hurdle. In order to show that they fell short of their duty of care, you will need to be able to show that in the circumstances, it was reasonably foreseeable by the contractor that the board could have been blown by the wind so as to cause property damage which we have discussed in more detail above. in the circumstances whereby you can show that the adverse weather was predicted, then I cannot see any reason why you could not show that the damage that has been caused was reasonably foreseeable and that as a consequence, the contractor was negligent in leaving the board out given the weather that was predicted.
as such, though there is an obligation upon you to mitigate any losses you claim, I cannot see any particular reason why you should not be able to make a full claim for indemnity in respect of any reasonable repair costs and other losses you suffer as a consequence of the contractor's apparent negligence. If this becomes necessary, and you cannot agree terms between you, then a claim can be made in the County Court in this respect:
https://www.gov.uk/make-court-claim-for-money