I use tungsten film (Portra 100T) with flash, but put a piece of full CTO (colour temperature orange, daylight to tungsten lighting gel) over the flash. If Im using faster tungsten film (Ektachrome 320T/EPJ or Eastman Vision2 Expression 500T/5229 both 35 mm only) I dont use flash.
If you have sunlight streaming through the window, that would look blue, of course. One answer, if that is not what you want to happen, is to cover the windows in CTO, perhaps with ND as well. Might you be better off using daylight film (and maybe reflectors) in this case?
Best,
Helen