The National Hurricane Center says the storm reached the coastline about 80 miles (128.74 kilometers) southeast of Tuxpan, Mexico, early Thursday with maximum sustained winds of 85 mph (136.79 kph).
Franklin strengthened into the first hurricane of the Atlantic season on Wednesday.
Authorities in Veracruz ordered classes canceled at public schools Thursday as a precautionary measure.
As a tropical storm, Franklin made a relatively mild run across the Yucatan Peninsula earlier in the week. Mexico Civil Defense director Ricardo de la Cruz said Tuesday that the storm’s impact on Yucatan was not as bad as initially feared, with some trees down and power out in some areas.
Mexico’s long eastern coastline is often struck by storms during the Atlantic hurricane season, which runs from June 1 through November 30.
In September 2013 Mexico was struck almost simultaneously by hurricanes Ingrid in the east and Manuel in the west, leaving some 157 dead in the southern state of Guerrero.