I am promoting a string of comments to a proper answer but it's probably important to note that jus sanguinis does not work quite in the way you describe. Countries do not usually “offer” citizenship to children of current citizens. Rather, they typically grant citizenship, at birth, to the children of citizens.
So if one of your parent is, for example, a French citizen at the moment of your birth then you are automatically a French citizen yourself (with some caveats, see below). You might need some paperwork to actually benefit from it in practice (e.g. to get a passport, vote, etc.) but you don't need to become a citizen later on; you already are one, from day one.
On the other hand, if your parents get French citizenship through naturalization after you have reached adulthood, France does not offer you anything. You are not a citizen and your parents' French citizenship won't even make it easier for you to become a citizen.
For jus sanguinis, it's therefore citizenship at the time of your birth that matters. Consequently, the grand-children of a French citizen would simply be French citizens from their birth, as would the parent that transmitted them the citizenship, without having to do anything to request it.
In the case of France, the big caveat is that if you don't do anything to actively avail yourself of this citizenship (e.g. by applying for a passport, this is called “possession d'état” in French) and reside outside of France for more than fifty years then your children will lose their French citizenship (article 30-3 of the code civil).
It does mean that some distant ancestry will not make you a French citizen but the relevant criteria is not the number of generations and the law is structured in a completely different way (it's not “you can be French if one of your ancestors up to that generation was French” but rather “all your descendants are French unless some specific condition is met”).
In practice, it probably means that France might not meet your requirements but you need to be careful about these details if you want to understand nationality law. The details vary but many countries do have some form of jus sanguinis on the books.