Most probably not, unless it is specifically stated in the manual that the camera supports SDHC. SDHC is downward compatible to SD but not the other way round, meaning a camera that supports SDHC can take SD, but a camera that supports SD (the old standard) cannot take SDHC.
Adding on to what Ziploc mentioned. If you seriously want to get SDHC. My advice would be to bring your old Panasonic FX01 camera to the shop and asked for a SDHC to try out to see if it works. take a few shots and see the results. on and off to make sure everything is working fine before you proceed to buy. Its just playing safe in my opinion.