The Aero Ica Cessna plane went down near a landing strip in Peru's southern desert and all five tourists aboard died, police chief Col. Guillermo Arteta told Canal N cable news channel. Local media reported the Peruvian pilot survived.
Arteta said the crash appeared to be the result of "human error." He said witnesses reported seeing the plane caught in high-tension cables before it crashed.
The names of the French tourists were not immediately released.
Juan Carlos Pavic, head of the civil aeronautics office of the Transportation Ministry, said the pilot's license was valid and the plane's paperwork up-to-date.
Aero Ica spokeswoman Angela Rosel said the Cessna aircraft crashed during a 30-minute flight over the Nazca lines.
The lines, mysterious markings etched into the desert sands more than a millennium ago, are one of Peru's top tourist destinations.
Tourists often take short flights on small airplanes for a better view of the lines. Lima-based Aero Ica runs 80 flights over the lines a day.
The Nazca lines cover a 35-mile stretch of desert some 250 miles south of Lima and were named a UNESCO World Heritage Site list in 1994.