Short answer. Yes. Article 976 provides that a person may represent him whose inheritance he has renounced, so giving up your father's estate does not bar you from taking his place in your grandfather's. The two estates are separate, and refusing one is not a refusal of the other.
What the law says
A person may represent him whose inheritance he has renounced.
Civil Code, Article 976 — Representing One Whose Inheritance Was Renounced. Read the full provision →
Seven words that settle it
The provision could hardly be shorter: a person may represent him whose inheritance he has renounced. It exists because the opposite conclusion is so tempting. Having walked away from your father's estate, it feels as though you have walked away from everything that might come through him, and families settling a grandfather's estate often treat an earlier renunciation as having closed the door. The Code says it did not. The renunciation operated on one estate, at one moment, and it has no effect on a succession that opens later in a different person's family.
Because you inherit from the grandfather, not from your father
The rule follows from how representation works. A representative does not take his parent's property; he steps into his parent's place and inherits directly from the person whose estate is being settled. Nothing passes through the father's estate on the way, which is why the father's own financial position is beside the point. That also answers the practical worry behind most renunciations. If you renounced because your father died insolvent, taking his place in your grandfather's estate does not revive those debts or expose the grandfather's property to his creditors.
The converse rule, which is easy to confuse
Keep this article apart from a different rule that sounds similar. What you may not do is renounce the estate you are being called to and still have your own children represent you in it — an heir who repudiates his share in a particular succession is not represented in that same succession. The distinction is about which estate the renunciation touched. Renouncing your father's estate leaves you free to represent him elsewhere; renouncing your grandfather's estate would take you and your line out of that one for good. Read any deed of renunciation with that difference in mind.
Check what the deed actually says
Find the instrument you signed and read it closely, because these documents are often drafted broadly and some purport to give up rights in more than the estate then being settled. Note which estate it identifies, its date, and whether it was executed before or after your grandfather's death — a renunciation cannot operate on a succession that had not opened yet. Then establish your father's death preceded your grandfather's, since representation depends on it. Bring the deed and both death certificates to whoever is settling the estate rather than relying on how the family describes what happened.