A film with modest contrast such as Kodak Portra 160 or Fuji Pro 160 S are most suitable.
Kodak used to make special low-contrast copy films in both black-and white and color, but not now.
But even back in the 1980s Kodak recommended the following procedure for amateurs for occasional copying with amateur color negative films.
Youd give the film a low-dose fogging exposure of totally unfocused white light, either before or after the main exposure, to reduce the overall contrast.
You needed a camera that allows double exposure on the same frame of film. The recommended starting point for flashing exposure was from -3f to -4f. You were advised to test various fogging exposures to determine which gave the best results.
I did the flashing exposure by setting the lens to infinity focus, using the aperture wide open or nearly so, and shooting a piece of flash-illuminated white foamcore or white paper from within a few inches from the lens. The source flash was set to the lowest power setting and moved back to achieve -4f to -3f at the white reflecting surface as determined with my flash meter.