The ancient, extremely inefficient L293D driver on that motor shield can handle only very small motors, with 0.6A maximum steady state current draw per channel.
The Pololu motors each briefly draw the start/stall current of 5.5A, 10X the rating of the L293D driver, every time they start moving.
Pololu sells modern, highly efficient MOSFET motor drivers. Select one that can easily handle the 5.5 A startup current.
Polulu page for that controller states: The M3S256 supports motor supply voltages from 4.5 V to 48 V and can deliver continuous output currents up to 2 A per motor .
IMO, give yourself some headroom and select a controller with double digit current output.
The Motoron M3S256, with peak instantaneous current 6.4A per channel, is barely adequate for the linked motor. If that is all you can afford, it will work, but as mentioned above, it is safer and more reliable to be generous in sizing motor drivers and motor power supplies.