What is a Renaissance and did the Carolingians have one?

Renaissance translates literally as a "re-birth" ("naissance" in French means "birth"). The Renaissance in 15th century Europe represented a "re-birth" of classical knowledge. It was a return to the ideas and thoughts of classical Greece and Rome and the rediscovery of pagan art, culture, and philosophy posed a challenge to the dominance of Church doctrine.
The Carolingian Renaissance was not really similar. This term refers to the time of the Empire of Charlemagne, who was the greatest king in Europe in the Middle Ages. Charlemagne unified the Frankish tribes and brought most of Europe (except Spain, which was occupied by the Muslims) under his control. He was crowned Holy Roman Emperor in 800 CE.
Charlemagne's Renaissance was a return to some of the culture of Rome. There was a restoration, briefly, of the Pax Romana. He also emphasized education. But the bulk of this rebirth was Christian. He forced those he conquered to convert at the point of a sword, and there were many barbarisms in his realm.
Regardless, by sponsoring scribes, learning to read and write, and emphasizing knowledge to some degree, Charlemagne "revived" a cultural civility in the so-called "Dark Ages".