Short answer. No. The invalidity of one disposition does not drag down the others. The remaining gifts stand on their own, unless it must be presumed the testator would not have made them had he known the invalid one would fail. Void provisions are severed; the valid ones are carried out.
What the law says
The invalidity of one of several dispositions contained in a will does not result in the invalidity of the other dispositions, unless it is to be presumed that the testator would not have made such other dispositions if the first invalid disposition had not been made.
Civil Code, Article 792 — Invalid Dispositions Are Severable. Read the full provision →
The valid gifts survive
Article 792 treats a will as a bundle of separable dispositions rather than an all-or-nothing document: the invalidity of one of several dispositions contained in a will does not result in the invalidity of the other dispositions. So if one legacy fails, because its object no longer exists, its beneficiary is disqualified, or the clause itself is unlawful, the rest of the will is not pulled down with it. Each gift is judged on its own footing, and the ones that are perfectly good are given effect. A single defective provision does not force the estate into intestacy.
The exception: interdependent gifts
The severability is not absolute. It yields unless it is to be presumed that the testator would not have made such other dispositions if the first invalid disposition had not been made. Where the gifts are so bound up that the valid ones were plainly conditioned on the failed one, the whole scheme may fall together. The test is the testator's own intention: were the surviving dispositions meant to operate independently, or only as part of an arrangement that no longer holds together once its central piece is gone? If the answer is the latter, they go with it.
Where the line usually falls
In practice most bequests are independent. A gift of a car to one child and a parcel of land to another do not depend on each other; strike one and the other is untouched. Interdependence is the exception and has to be shown, not assumed, from the terms and structure of the will, an integrated plan of distribution, a gift expressly made in exchange for or in reliance on another. The presumption favours saving the valid dispositions, so the party arguing that everything collapses carries the burden of demonstrating the linkage.
What this means for you
If one gift in a will you are relying on turns out to be void, do not assume your own bequest is lost. Look at whether your gift stands by itself or was tied to the failed one in the testator's design. The property under the invalid disposition does not simply vanish either; unless the will provides for it, it typically passes as if there were no will as to that portion, to the intestate heirs. These questions are resolved at probate, on the face of the will and its structure, so the drafting is what settles them.