Short answer. The rest passes by intestate succession to his legal heirs. Article 851 says that where a will institutes an heir to only an aliquot part of the estate, legal succession takes place over the remainder. The will governs the part it disposed of; the law distributes whatever it left untouched.
What the law says
If the testator has instituted only one heir, and the institution is limited to an aliquot part of the inheritance, legal succession takes place with respect to the remainder of the estate.
Civil Code, Article 851 — Sole Heir Instituted to Part of the Estate. Read the full provision →
What Article 851 provides
Article 851 provides that if the testator has instituted only one heir, and the institution is limited to an aliquot part of the inheritance, legal succession takes place with respect to the remainder of the estate. The same rule applies where several heirs are each instituted to an aliquot part and the parts do not cover the whole. In plain terms: a will does not have to dispose of everything. Where it hands out only a fraction — a half, a third — the fraction it did not reach is not left in limbo. It devolves as if there were no will over that part.
Testate and intestate succession side by side
This is the law's answer to a partial will, and it shows that testate and intestate succession can operate over the same estate at once. The portion the will actually gave away goes to the instituted heir on the will's terms. The remainder — the part the testator, by using an aliquot fraction, did not dispose of — passes to his legal or intestate heirs under the rules that apply when someone dies without a will. So your father's estate may be split: one slice moving under his will, the rest moving under the intestacy rules, each governed by its own regime.
Who the remainder actually goes to
The leftover does not go to the instituted heir by way of bonus, and it does not go to the State while family survives. It goes to the intestate heirs, in the order the law lays down — legitimate children and descendants first, then ascendants, then the surviving spouse and collateral relatives, in the combinations the Code sets. The instituted heir may well also be an intestate heir, in which case he shares in the remainder too, but as a legal heir and not because the will said so. Identifying who stands in that intestate order is the key to who takes the untouched part.
The compulsory-heir dimension
One thing to watch is whether the will's partial gift trespassed on anyone's legitime — the share the law reserves for compulsory heirs such as children and the spouse. Article 851 sorts out an estate the testator simply under-disposed of; it does not by itself cure a gift that shortchanged a forced heir, which is dealt with separately. So work in two steps: apply the will to the fraction it covered, run the remainder through the intestate order, then check that the compulsory heirs received at least their reserved shares across the whole estate.