Make sure the fireplace damper is closed. In a tight home A fireplace will snag air anywhere it can find it. If the furnace is in a unheated place you might cancel the draft.
In a fix a draft inducer will work. I've had to use them when the furnace was near a commercial kitchen.
Because the water is on the flue also it should keep the flue warm enough to draft. If it's back drafting also I'd probably look for whatever is causing a negative pressure in the home.
"What Fools these mortals be"....Puck