This paper introduces the novel concept of a cross dipole nanoantenna for use in fluorescence based sensing applications. The dual-arm nature of the cross nanoantenna allows a dual resonant structure to be designed such that the shorter arm resonates with the pump wavelength and the longer arm with the emission wavelength. This is expected to further enhance emission from any fluorescent molecule that can couple to both nanoantenna arms when compared with a singly resonant structure. The paper uses the finite-difference time-domain method to first analyze the two-arm nanoantenna case and then shows how intensity enhancement depends on the antenna geometry and tapering of arms in the antenna gap. The results show that smaller gap sizes always produce larger enhancement compared with lightning rod effects due to tapering. A four-arm cross nanoantenna is then studied, highlighting differences from the two-arm case. Finally, the effect of a diagonally aligned molecule transiting the central gap region is studied. The results show that two hotspots occur on either side of the central gap region when the molecule is aligned perpendicular to the transit direction and only a single central hotspot occurs when the alignment is parallel to the transit direction.