Franklin has weakened to a tropical storm as it moves farther inland over eastern Mexico.
"We're now entering the peak of the season when the bulk of the storms usually form", said Gerry Bell, lead seasonal hurricane forecaster at NOAA's Climate Prediction Center, in a statement.
The U.S. National Hurricane Center says Franklin's maximum sustained winds later decreased to near 70 miles per hour with additional weakening expected.
"At this time, the more likely scenario is for the tropical system to stay offshore", AccuWeather meteorologist Dan Kottlowski said in a report.
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.
After dissipating over Mexico, remnant energy from Franklin may help spawn another tropical depression or tropical storm in the eastern Pacific in the days ahead.
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Hurricanes in the Atlantic are named based on a list that rotates every six years.
A year ago, eastern Mexico was ravaged by flooding and mudslides from Tropical Storm Earl which claimed the lives of 81 people.
A hurricane warning was in effect for the coast from Veracruz city north to Cabo Rojo.
Franklin strengthened into the first hurricane of the Atlantic season Wednesday as it neared Mexico's central Gulf coast, heading for an overnight landfall that would be its second on Mexican territory in three days. This surge could also bring "large and destructive waves".
There are two primary reasons for the increase in predicted tropical activity since the start of the current tropical season.
An estimated $28.3 trillion worth of homes, businesses and infrastructure in the 18 Atlantic coastal states are vulnerable to hurricane strikes. That's slightly above the 11 to 17 named storms and two to four major hurricanes predicted at the start of the season. The 2017 hurricane season officially began June 1 and ends November 30.