Thousands of people gathered to watch in the port of Saint-Nazaire, in western France, as the 230ft high vessel was guided out to sea by six tugs on March 10.
The €1 billion ($1.1 billion) ship is being built for the Royal Caribbean International (RCI) cruise company.
Harmony of the Seas, a 120,000-tonne vessel, is expected to be delivered to the RCI in two months.
The sea trial will continue until March 12.
The 16-deck Harmony of the Seas is 362m long – 50m longer than the Eiffel Tower is high.
After completion, Harmony of the Seas will be able to accommodate more than 6,000 passengers.
About 2,000 crew members will cater for their needs.
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