The City of Fort Worth having heretofore entered into contracts for the pavement of streets or begun proceedings looking thereto, all provisions of the preceding Charter and ordinances of the City of Fort Worth providing for the construction of such improvements or assessment of the cost thereof against owners of abutting property and their property, or the enforcement of such assessment shall remain in full force for the purpose of effecting the construction of the said improvements and assessing and collecting the cost thereof, and all contracts entered into by the City of Fort Worth heretofore for the same are hereby validated.