Short answer. No. Where a second will expressly revoked the first, revoking the second does not revive the first. The first will can be revived only by another will or codicil. Undoing the second instrument leaves the first still revoked; you must positively re-make or republish it to give it effect again.
What the law says
If after making a will, the testator makes a second will expressly revoking the first, the revocation of the second will does not revive the first will, which can be revived only by another will or codicil.
Civil Code, Article 837 — No Automatic Revival. Read the full provision →
No automatic revival
Article 837 rejects the intuition that cancelling the replacement restores the original: if after making a will, the testator makes a second will expressly revoking the first, the revocation of the second will does not revive the first will, which can be revived only by another will or codicil. The express revocation in the second will did its work and killed the first. When you later revoke the second, you remove the second will, but you do not resurrect the first. It stays revoked, and the estate is not governed by it merely because the instrument that displaced it is now gone as well.
Why the law refuses to guess
The rule spares the courts from having to infer what a testator wanted from a sequence of cancellations. A person who revokes his second will has told us only that he no longer wants the second will; he has not told us he wants the first one back. Perhaps he does, perhaps he prefers to die intestate, perhaps he means to write something new. Rather than read a revival into his silence, the law requires him to say so affirmatively. Intention to revive must be expressed in a proper instrument, not deduced from the mere undoing of the later will.
How to actually revive the first will
Revival is available, but only by a positive testamentary act. The first will can be brought back by another will or codicil, either one re-executing its dispositions, or a codicil that refers to it and republishes it. Both routes require the reviving instrument to be executed with full formalities. So if the first will expresses your real wishes, the step is to make a new will or codicil reinstating it, not to rely on the revocation of the second having cleared the way by itself.
What governs in the meantime
Until such a reviving instrument exists, the position is that both wills are ineffective: the first revoked by the second, the second revoked by you. If nothing else is executed, the estate passes by intestate succession, under the shares the law fixes when a person leaves no operative will. So check whether any later valid will or codicil reinstating the first was ever made. If none was, the estate is settled as an intestate one, whatever the first will originally said.