Trouble programming ATMEGA328 via FTDI cable

No that should be fine - so assuming the xtal is running ok on 3.3V it should work - but reset is an issue with modern bootloader you have 1/2 a second or so to press the button if auto-reset isn't working.

That Oomlout circuit seems to be wrong - CTS isn't grounded so it'll float leading to intermittent operation - it should be at logic 0 to allow the FTDI chip to send serial to the 328. Connect a 100nF cap between RTS pin and the reset pin and you should get auto-reset too...