Short answer. Yes. Article 515 gives the landowner the choice between doing the repairs himself or permitting the affected neighbors to do them without damage to him. If he refuses to do the work himself, he must at least permit the exposed neighbors to carry it out on his land.
What the law says
The owner of a piece of land on which there are defensive works to check waters, or on which, due to a change of their course, it may be necessary to reconstruct such works, shall be obliged, at his election, either to make the necessary repairs or construction himself, or to permit them to be done, without damage to him, by the owners of the lands which suffer or are clearly exposed to suffer injury.
Civil Code, Article 515 — Duty To Maintain Defensive Works. Read the full provision →
The owner has a choice, but not the choice to do nothing
Article 515 puts the landowner in a position where inaction is not an available option. The article states the owner "shall be obliged, at his election, either to make the necessary repairs or construction himself, or to permit them to be done, without damage to him, by the owners of the lands which suffer or are clearly exposed to suffer injury." The word "obliged" makes clear that one of these two paths must be taken — simply refusing to act and refusing to let others act is not an option the article allows.
Refusing to do the work yourself does not end the matter
If the landowner elects not to perform the repairs or reconstruction personally, the article's structure means the second branch of the obligation takes over: he must permit the affected neighbors to carry out the necessary work themselves. This is exactly the situation you describe — a landowner declining to rebuild the flood-defense works does not get to also block the exposed neighbors from doing it, because the article frames these as the owner's only two available choices.
Who counts as an affected neighbor under this article
The right to step in and do the work belongs specifically to "the owners of the lands which suffer or are clearly exposed to suffer injury." This covers neighbors who are already experiencing harm from the lack of proper defensive works, as well as those who have not yet been harmed but are clearly at risk of injury from the same failure to maintain or rebuild the works. Someone with only a speculative or remote connection to the risk would not fall within this description.
The work must be done without damage to the owner
The permission the article grants is qualified: the work by the neighboring owners must be carried out "without damage to him," meaning to the landowner whose property the work takes place on. This does not mean the landowner can impose unreasonable conditions to defeat the purpose of the article, but it does mean the neighbors undertaking the repairs should carry out the work in a way that does not needlessly harm the landowner's property beyond what the necessary repairs themselves require.