How about a closer-co-operating Germany and France? German Army buys the AMX-13 and VCI series instead of the M113, and the French Army buys the Leo-I instead of the AMX-30.
OR, IRL, I couldn't see the British Army buying them because at the time, they thought they had to have a British-style right-hand driving position, hence developing the FV432 instead of buying the M113, while the AMX-13 had a left-side one. However they subsequently abandoned this idea (see the Warrior) so what if they abandoned it earlier? You could see the British Army buying the AMX-13 and VCI. Perhaps that might lead to the turreted version of the F2 105mm SPG going into production (only got as far as a prototype IRL) instead of the Abbot.
In whiff-world, you could "sell" AMX-13s to any real-world users of Chaffees, Walker-Bulldogs, Saladins, Scorpions or PT-76s.