1. A nucleic acid analysis method comprising the steps of: irradiating, with light, an analysis sample including a plurality of DNA fragments; detecting fluorescence, excited from the analysis sample, corresponding to the DNA fragments with an imaging element within a predetermined detection time; setting a lower limit of fluorescence intensity required for analysis of the analysis sample within a detectable range of fluorescence intensity of the imaging element; acquiring fluorescence intensity for each of the DNA fragments based on the lower limit; detecting a peak of the fluorescence intensity acquired for each of the DNA fragments and determining time information corresponding to the peak; and displaying correspondence of the fluorescence intensity to the time information for each of the DNA fragments, wherein the display displays at least one or more peaks including a first peak having first fluorescence intensity and a second peak having fluorescence intensity weaker than the first fluorescence intensity, and the lower limit is adjusted with a predetermined value and fluorescence intensity, where measurement is made using the adjusted lower limit as the lower limit of the imaging element, is reset as fluorescence intensity of at least one or more peaks including the second peak, thereby determining whether at least one or more peaks including the second peak are false signal peaks.