Hi,
Assuming you're running the PICaxe from a 5 volt regulator then almost any "Logic Level" FET will do. But below about 4 volts, rather more care may be needed. The 2N7000 is a simple, general purpose, low-cost FET, perhaps not quite good enough for a full 400 mA alone, but you could put a few in parallel. Others may have their own particular "favourites".
In practice a bipolar (NPN) transistor or a relay can do much the same job. They may appear less efficient (requiring an additional current into the base or coil) but the main loss of useful energy is in the LEDs' (essential) series resistor. For best efficiency you could use a switched-mode constant-current driver, but that's a considerable complication. Also, you may prefer that when/if the 12v battery voltage falls, the LEDs get dimmer (extending the remaining life) as happens with a simple resistor.
Cheers, Alan.