It wasn't really a question of some units' uniforms having the coats turned back and others not. Either is perfectly correct for any French infantry unit of this period.
There were two factors at work: practicality and evolving fashion. In terms of practical wear, we might expect to see the coat tails hanging loose in cold weather, as it provided more warmth to the upper legs. Contemporary and later illustrations show this for the armies of the time, not just the French.
However fashions were evolving, which made the turned-back style more likely later in our period. Military fashion was set by Prussia at this time and Frederick's soldiers got issued with coats that were increasingly tight and skimpy throughout his reign. There were two reasons for this. Firstly saving on the total amount of cloth needed to make up uniform coats; woollen cloth was surprisingly expensive as a commodity at this time, compared to daily living costs, so every inch saved meant a financial economy. Frederick was notoriously "careful" with his money! Secondly, Prussian military clothing acquired a somewhat different look in the time of Frederick's father, the "soldier king". He disliked the contemporary fashion of full skirts, huge cuffs and so forth, seeing it as effeminate, "too French" and unsoldier-like. This process continued under Frederick, so that eventually the coats could not be buttoned up at the front, for example, as there just wasn't enough material in them. I don't think the turnbacks were actually stitched on, at least until after the SYW, but they became impractical to turn down. When Prussia won victory after victory under Frederick, other armies came gradually to copy the Prussian style. Even the French. This process accelerated during the SYW.
Thus by 1763, most infantry soldiers, were more likely to have the coat tails turned back, even in colder weather. But unless you want to very specifically portray a particular timespan within the period, then either look is perfectly fine for any or all units.