The former mayor of Central Falls has agreed to pay a $7,000 fine and admit he violated ethics rules when he accepted a new furnace from a campaign contributor who got a lucrative city contract. The state Ethics Commission voted unanimously Tuesday to approve the agreement with Charles Moreau. Moreau pleaded guilty in November to a federal corruption charge related to the gift and is scheduled to be sentenced next month. Moreau’s agreement with ethics officials ends a years-long ethics investigation of the former mayor, who stepped down last year. Moreau accepted the nearly $7,000 furnace and home repair work from Michael Bouthillette, who received a no-bid contract to board up vacant houses.