FT232 in battery operated device
Power the FT232 from USB (it's of no use when USB is not connected anyway).
Power the battery charger directly from USB too, not through FT232.

You can also power the rest of the system directly from USB (through an extra regulator) if you add some power path switching to avoid short-circuiting USB and the battery when both have power. This has the advantage of not drawing current from the battery while also charging, as that can confuse the charger somewhat (although the charger will still work). There are ICs that conveniently solve this by charging the battery and selecting where to power the system from.

Optional: To fully comply with the USB specifications, you should not draw more than 100 mA without first negotiating this with the host. (In this case, configuring FT232 to do the negotiation for you and outputting on a pin when it's ok to draw more current.) USB also specifies that the load should draw very little current when the USB bus (= the host) goes into suspend mode, i.e. a laptop is put into power-save.

Devices commonly ignore these additional requirements but I mention them just so you know.

EDIT: The easiest "power path switching" to select between USB and battery power is two diodes, one from each power source. The source with highest voltage will power the system. Use schottky diodes to minimize the voltage drop, for example a double component like TBAT54C,LM. This will cost you around 0.4 V, which reduces the useful capacity of the battery somewhat. More competent solutions use transistors to enable a low-resistance path from only the active power source -- or again, a battery management IC with built-in power path selection.

EDIT 2: TBAT54C,LM is not a good choice as you stated system current draws 500 mA and this is above the rated limit of TBAT54C,LM.