Short answer. No — the heir does not lose the inheritance. Article 873 says impossible conditions, and those contrary to law or good customs, are considered as not imposed and shall in no manner prejudice the heir, even if the testator provided otherwise. The illegal condition is simply struck out, and the heir takes the inheritance free of it.
What the law says
Impossible conditions and those contrary to law or good customs shall be considered as not imposed and shall in no manner prejudice the heir, even if the testator should otherwise provide.
Civil Code, Article 873 — Impossible and Unlawful Conditions. Read the full provision →
The condition is disregarded, not the gift
Article 873 answers the worry directly. It provides that impossible conditions and those contrary to law or good customs shall be considered as not imposed and shall in no manner prejudice the heir. In succession, an unlawful or impossible condition attached to what you leave someone is treated as if it were never written. The inheritance itself is not cancelled along with the bad condition. Instead the condition drops out and the heir receives the property as though the will had simply given it outright. So attaching an illegal condition does not disinherit the heir; it only fails to bind him.
Even against the testator's contrary wish
The article goes out of its way to say the rule holds even if the testator should otherwise provide. That means you cannot escape the rule by declaring in the will that the heir must forfeit the inheritance if the illegal condition is not met, or that the condition is essential. The law overrides such a provision. Its policy is to favor the transmission of the estate to the named heir rather than to let an unlawful or impossible demand defeat the gift. A testator's insistence on the condition, however emphatic, does not convert an unenforceable condition into a valid ground for the heir to lose what was left to him.
Why wills are treated this way
This is a distinctive feature of testamentary gifts. In some other conditional arrangements, an impossible or unlawful condition can taint or annul the very obligation it is attached to. Succession law takes the opposite course, protecting the heir and preserving the disposition by simply erasing the offending condition. The reasoning is that a will speaks after the testator is gone and can no longer clarify or adjust his wishes, so the law leans toward giving effect to the gift while refusing to enforce a demand the law will not countenance. The heir benefits from that policy choice, keeping the inheritance while the condition is ignored.
What the rule does not do
Article 873 strikes only conditions that are genuinely impossible, or contrary to law or good customs. It does not free an heir from conditions that are merely burdensome yet lawful and possible — those remain effective and must be complied with. Nor does it validate a disposition that fails for some independent reason, such as a defect in the will itself or an impairment of the compulsory heirs' protected shares. Its narrow office is to neutralize a bad condition so that it cannot harm the heir. Within that scope it is protective; outside it, the ordinary rules on wills, heirs, and their legitimes continue to apply.