No, that is not who the Merovingians were.
The Franks were a confederation of the tribes which had been shattered by the Roman incursions into Gaul and across the Rhine River. Many of these tribes--the Ubii, the Treverii, the Chattii, the Suebii and the Cheruscii to name a few--became peaceful citizens of the Roman empire, but many others refused to submit to the Romans. Driven east, they collided with the Germanic tribes east of the Elbe. Reduced in numbers so that no one tribe could hold their own alone, they formed a confederation of "free men"--the word for which was frank--and called themselves the Franks. Tacitus tells us that German tribes often had a royal family upon whom they would call for leadership in times of war. The German tribes apparently did not have continuously enthroned kings, and might have appointed a powerful war leader to be the
Graf in times of crisis, if they mistrusted the leader of the "royal family."
Beginning in the fifth century, the Franks--now split into two main bodies, the Salian Franks (dominant) and the Ripurian Franks (referring to the new homelands they took up in the valley of the Rhine)--began to cross the Rhine into what is today France. Among the Salian Franks, the royal family were the Mervings. When the Huns marched across northern Europe to what is now northern France, the Roman General Aetius (who was probably of German descent) organized a defense by calling on the Franks to fight with him, and offering them a federation in the empire, a common practice in which the Romans would give land to a "barbarian" tribe which would fight on behalf of the empire. Aetius also appealed to the Visigoths, the Alans and the Burgundians. In a battle which is believed to have taken place near Chalons in 451 CE, Aetius fought the Huns to a draw, and Attila was forced to retreat. Attila's influence began to wane thereafter, and the Huns never again threatened the west.
At that time, the Franks chose one of the Mervings as their war leader, and the Romans referred to him as "Merovius" or "Merobius"--hence, the term Merovingian. Taking the decidedly "un-German" idea of an hereditary monarch, the Mervings, now called Merovingians, made themselves, at least nominally, the Kings of the Franks.
You can read about the historical Merovingians in this Wikipedia article.
A few of the Knights Templar in later days decided to refer to themselves as Merovingian because of an unsubstantiated claim that they were descended from the "true" Kings of France. It was nonsense then, and it is even bigger nonsense now. Almost everything you will hear or read about the Knights Templar these days is horsie poop, cobbled together from historical half-truths and outright myths. Conspiracy lovers just gobble this poop up.
Click here to read the contemporary "official" story of the Knights Templar referred to as Merovingians.
Anyone who thinks there is even an ounce of historical truth in the story of the Knights Templar who called themselves Merovingians is invited to peruse this colorful brochure i have about a bridge in New York i am willing to sell at a discount.