Left altar radical (the side-form of 示), picturing the stone tablet of an ancestral altar. Marks 福 as a ritual/divine-blessing character: good fortune comes through the altar from gods and ancestors. Same radical anchors 神 (deity), 祖 (ancestor), 礼 (rites), 祝 (pray).
Right-side 畐 supplies the sound (matches parent fú exactly) and a strong semantic. Standalone 畐 pictures a brimming wine jar - abundance. So 福 reads 'altar plus full vessel': blessing flows from offering a full jar to the gods. Same phonetic: 富 (rich), 副 (deputy), 幅 (width).
