1. A fluorescence endoscope device comprising: a light source that irradiates a subject with excitation light and illumination light; a fluorescence-image acquisition portion that captures an image of the fluorescence generated at the subject due to the irradiation with the excitation light from the light source to obtain a fluorescence image; a reference-image acquisition portion that captures an image of return light returning from the subject due to the irradiation with the illumination light from the light source to obtain a reference image; a divided-fluorescence-image generating portion that divides the fluorescence image by the reference image to generate a divided fluorescence image; a first-region extracting portion that extracts a first region having a gradation value higher than a first threshold in the fluorescence image; a second-region extracting portion that extracts a second region having a gradation value higher than a second threshold in the divided fluorescence image; a corrected-fluorescence-image generating portion that generates a corrected fluorescence image in which an overlap region, where the first region of the fluorescence image extracted by the first-region extracting portion overlaps the second region of the divided fluorescence image extracted by the second-region extracting portion, is extracted from the fluorescence image; and a display portion that displays the corrected fluorescence image generated by the corrected-fluorescence-image generating portion.