In the eighteenth century, M. de Kemur, Sire de Legal, is said to have invented this game. It has had its occasional bursts of popularity; Pritchard mentions popularity in the Regence, where Labourdonnais and Deschappelles are said to have played many games, and calls this game The Pawns Game; the name Sixteen Pawns is taken from Michael Kellers World Game Review.
Both Labourdonnais and Deschappelles were famous and very strong chess players. Labourdonnais beat MacDonnell in the longest series of recorded games played before Karpov met Kasparov, and the games are still famous and still anthologized. When you extend the world championship backwards, you find that Labourdonnais is the champion after Philidor and before Staunton.
Deschappelles was stronger than Labourdonnais, but he probably never played outside of France; Deschappelles was very very strong, and he also played Whist (the card game), in which he invented a play still in use in modern bridge; the Deschappelles Coup is rarely seen, and only strong bridge players (and some chess players, of course) ever have heard of it.
The normal rules of chess are applied, with the following exception: white does not have a queen, but gets eight additional pawns instead, i.e., white has sixteen pawns, hence the name of this game.
White may place these eight additional pawns arbitrarily on the third and fourth row. Only the white pawns that are on the second rank may make an initial double step.
White may choose himself where he places the eight additional pawns. Below, some sample setups are shown.
One can give White a pawn extra or less, for a handicap when playing with players of unequal skill.
After experimentation, it was pretty well established by Labourdonnais and Deschappelles that 8 Pawns are much too strong; probably they played with five or six or seven extra Pawns. Five sounds like too few, but in fact the side with the Pawns has a positional advantage in addition to the material (a stronger Pawn formation!)