Short answer. No, generally. The Civil Code says that when a will orders more than the actual amount of a specified debt paid, the excess is not due — unless a contrary intention appears from the will itself showing the testator meant to give the extra as a gift.
What the law says
If as regards a specified debt more than the amount thereof is ordered paid, the excess is not due, unless a contrary intention appears.
Civil Code, Article 939 — Paying a Debt the Testator Believed He Owed. Read the full provision →
The default rule caps payment at the actual debt
Article 939 addresses this exact situation: a will that orders more than the amount of a specified debt to be paid. The default answer is that the excess is not due — the estate is not obligated to pay beyond what was actually owed, even though the will's wording says otherwise. The law treats the overstatement as, most likely, a mistake about the true amount rather than an intended additional gift.
A contrary intention can change the outcome
The rule is not absolute. Article 939 allows for the excess to become due if a contrary intention appears — meaning if it is shown that the testator actually meant to give more than the debt itself, perhaps as an additional bequest layered on top of settling the debt, rather than simply being mistaken about the amount owed. Where that intention is evident, the excess is treated as a deliberate gift rather than an error to be corrected.
This sits beside a related rule on debts that never existed
Article 939 opens with a related but distinct situation: if the testator orders payment of something they believe they owe but do not in fact owe at all, that disposition is considered as not written — meaning it simply has no effect. The excess-payment rule that answers your question is the next step in the same logic: where a real debt exists but the will overstates its amount, only the actual amount remains payable as debt, with the overstated portion falling away unless shown to be intentional.
Natural obligations are not affected by this article
Article 939 closes with a qualification that applies to both of its rules: they are without prejudice to the fulfillment of natural obligations. This means that even where a disposition is treated as not written, or an excess is found not due under this article, that does not by itself extinguish a separate natural obligation that might independently support payment — this article addresses testamentary dispositions specifically, not every possible basis for owing something, so a claim resting on some genuinely separate and independent foundation remains unaffected by either of these two rules.