No you can not program it with an "FTDI programmer", these are not programmers they are just USB to UART (OR TTL level serial or whatever you choose to call it), they are not a programmer, they facilitate you to communicate with a "virtual" programmer we call a bootloader which you or somebody has installed on a chip.
The ATTiny26 does not support self programming, so even if you put on a bootloader you still can't use one of those.
You need an ISP programmer, such as the USBasp, or if you must, you can get away with using another Arduino and the ArduinoISP sketch, but really, just get a USBasp.
Note that the Tiny26 is not a common chip to be using, at least not in Arduino circles. You will probably find it better to stick with the following...
ATtiny25
ATtiny45
ATtiny85
ATtiny24, ATtiny24A
ATtiny44, ATtiny44A
ATtiny84, ATtiny84A
ATtiny13, ATtiny13A
NB: I have an easy to install Arduino core for the above chips here -
https://github.com/sleemanj/optiboot/tree/master/dists#attiny