Espoir seems to be more focused, and more tangible. Espérance refers more to a state of mind, more like optimism. Espoir is widely used in French, as opposed to espérance which is a not-so-used word.

ex. J’espère (j’ai l’espoir) que le repas sera bon (I hope the meal will be good). vs Il est plein d’espérance (he is full of hope)

while “espoir” (https://fr.wiktionary.org/wiki/espoir) -which is the “Déverbal” of “espérer”- is a neutral,abstract,down-to-earth and everyday life word,”espérance”(https://fr.wiktionary.org/wiki/esp%C3%A9rance) is formal and more focused on the action by itself…

In deed,”espérance” can be split into the stem that comes from “espérer” plus the sufix “-ance” which gives all the nuance to that word :the sufix “-ance” indicates an action or the result of an action (https://fr.wiktionary.org/wiki/-ance).
“espérance” is widely used in theological literacy and mathematics :

l’espérance mathématique d’une variable aléatoire réelle est, intuitivement, la valeur que l’on s’attend à trouver, en moyenne, si l’on répète un grand nombre de fois la même expérience aléatoire

(https://fr.wikipedia.org/wiki/Esp%C3%A9rance_math%C3%A9matique)

Finally,i dare say that “espérance”” is for situations in which we are sure about the result while “espoir” has a nuance of great uncertainty.

Correct usage is L’espérance de vie and not L’espoir de vie that could help clarify usage for both. That’s how I came to this anyway, always thought the correct term was “espoir de vie”

Espoir est horizontal, espérance est vertical. Espoir is horizontal (concrete, grounded, material…), while espérance is vertical (spiritual, inspirational, greater…)