Short answer. The owners of the nearest riverbanks. Article 465 gives such an island to the owner of the nearest margin, or divides it longitudinally in half between both bank owners if it forms in the middle. If it forms closer to one side, that side's owner takes the whole island.
What the law says
Islands which through successive accumulation of alluvial deposits are formed in non-navigable and non-floatable rivers, belong to the owners of the margins or banks nearest to each of them, or to the owners of both margins if the island is in the middle of the river, in which case it shall be divided longitudinally in halves.
Civil Code, Article 465 — Islands on Non-navigable Rivers. Read the full provision →
What the law says
If a single island thus formed be more distant from one margin than from the other, the owner of the nearer margin shall be the sole owner thereof.
Civil Code, Article 465 — Islands on Non-navigable Rivers. Read the full provision →
Ownership follows proximity to the riverbank
Article 465 assigns ownership of a gradually formed island based on where it sits relative to the riverbanks. Islands which through successive accumulation of alluvial deposits are formed in non-navigable and non-floatable rivers, belong to the owners of the margins or banks nearest to each of them. The basic principle is proximity: whichever bank the island sits closest to, that bank's owner is the one who acquires it, since the accumulation is treated as an extension of the nearby land.
An island in the middle is split down the middle
The article addresses the situation where the island does not sit closer to either side. Or to the owners of both margins if the island is in the middle of the river, in which case it shall be divided longitudinally in halves. Rather than picking one owner arbitrarily, the statute splits the island lengthwise, giving each riverbank owner an equal half, matching the balanced position of the island itself between the two banks.
Closer to one side means sole ownership for that side
Where the island is not exactly centered, the rule shifts decisively rather than applying a proportional split. If a single island thus formed be more distant from one margin than from the other, the owner of the nearer margin shall be the sole owner thereof. Even a small difference in distance is enough to give the entire island to the nearer bank's owner — there is no partial or proportional allocation once one margin is established as closer than the other.
Why this article specifically requires a non-navigable, non-floatable river
The rule is limited by its own terms to rivers that are not navigable or floatable. This distinction matters because navigable and floatable rivers are generally treated as public in a way that changes how accretions and formations within them are owned, so the private-ownership rule this article sets out does not automatically extend to islands forming in rivers that carry that public character.