Short answer. Yes. A compulsory heir left less than his legitime by any title may demand that it be fully satisfied. You are not put to a choice between accepting the shortfall and attacking the will — the remedy the Civil Code gives you is completion of what is missing.
What the law says
Any compulsory heir to whom the testator has left by any title less than the legitime belonging to him may demand that the same be fully satisfied.
Civil Code, Article 906 — Completion Of Deficient Legitime. Read the full provision →
The remedy is completion, not annulment
This is the most misunderstood point. Being short-changed does not make the will void, and you do not have to have it struck down to get your share. The article gives a targeted remedy: the deficient legitime is fully satisfied, meaning topped up to what the law says it should be, while the rest of the testator's arrangements stand as far as they can. Attacking the whole will is a different fight with different grounds, and it is usually not the one a short-changed heir needs.
'By any title' closes the obvious loophole
The phrase by any title is doing real work. It does not matter whether what you received came to you as an instituted heir, as a legatee of a specific thing, as a devisee of land, or under some other label the will used. What is compared is value received against legitime due. So a testator cannot defeat the legitime by dressing a small share up in a different form, and an heir who received something is not treated as having accepted less than the law guarantees merely because the gift was named differently.
You have to know the number before you can claim it
The right is to the shortfall, so everything turns on two figures: what your legitime actually is, and what you in fact received. The first depends on which compulsory heirs survived — children, a surviving spouse, ascendants — because the fractions shift with the combination. The second depends on the valuation of what the will gave you. Neither is obvious from reading the will alone, which is why these disputes are usually really arguments about valuation and about who else is in the class of compulsory heirs.
What to gather
You will need the will itself, the death certificate, proof of your relationship to the testator, and the fullest picture of the estate you can assemble — titles, bank records, share certificates. Add anything showing gifts the testator made during his lifetime, because those can change the base against which legitimes are computed. Raise the shortfall in the settlement proceeding rather than signing a partition that records you as satisfied; a signed agreement is far harder to undo than a claim made before it.