Short answer. By the rules on co-ownership. Article 2170 says that when an accident or other fortuitous event commingles movables belonging separately to two or more people, the resulting mass is governed by co-ownership. No one loses their stake; instead each becomes a co-owner in proportion to what they contributed to the mixture, and they can later divide it.
What the law says
When by accident or other fortuitous event, movables separately pertaining to two or more persons are commingled or confused, the rules on co-ownership shall be applicable.
Civil Code, Article 2170 — Movables Carried Off by a Fortuitous Event. Read the full provision →
Accidental mixing creates co-ownership, not forfeiture
When a flood, fire, or similar mishap throws together goods that belonged separately to different owners, the law does not hand the whole mass to whoever ends up holding it. Article 2170 provides that when by accident or other fortuitous event, movables separately pertaining to two or more persons are commingled or confused, the rules on co-ownership shall be applicable. Nobody is stripped of their property simply because it can no longer be physically told apart. Instead, the mixed mass is treated as owned in common by the people whose goods went into it.
Each share is proportional
Co-ownership here is not equal ownership; it is proportional. Each person owns an undivided share of the combined mass measured by the value or quantity of what they contributed. If your goods made up a third of the mixture, you own a third of it in common with the others. This keeps the accident from enriching one owner at another's expense, because the arithmetic of contribution, not luck or possession, decides how much of the pooled property each person can claim.
No fault means no penalty
The rule applies precisely because the mixing happened by accident or fortuitous event, with no one to blame. Since neither owner caused the confusion, neither is penalised and neither gains a windfall. This is different from a situation where someone deliberately or carelessly mixes another's goods with his own, which the law treats less kindly toward the wrongdoer. Under Article 2170 the innocent commingling simply converts separate ownership into shared ownership of the whole.
Dividing the mass later
Being co-owners, the parties are not locked together forever. As with any co-ownership, they may agree to separate the mass, sell it and split the proceeds according to their shares, or otherwise partition their interests. If they cannot agree, the general remedies available to co-owners apply. The practical takeaway after such a mishap is to establish, as clearly as the circumstances allow, how much each person contributed, because that proportion is what governs both present ownership and any later division.