A method for making a film bag with reinforced bag seams includes a film extruder that produces a continuous tube of film. A flattener produces a continuous web of flattened film which has an upper surface and a lower surface. A fold maker has a receiving portion positioned above the web and a displacing portion is positioned below the web that moves cyclically upward to a first position to locate a portion of the web into the receiving portion, thereby forming a fold. A fold retention device prevents the fold from opening. A presser flattens the fold against the web. A sealer seals through the fold, forming a reinforced bag seam. A cutter severs a sealed portion from an unsealed portion of the web. A transport mechanism moves the film from the extruder, through the flattener, into the fold maker, beneath the presser, into the sealer and to the cutter.