How would you say something like this in French:
I hope that I can return (or pay back) your kindness (your favor)
You could say
J'espère pouvoir te/vous rendre la pareille.
or, more figuratively
J'espère pouvoir te/vous renvoyer l'ascenseur. (= I hope I can send you back the elevator)
You could also say:
Merci ! À charge de revanche !
Meaning you intend to return the favour (= payback, revenge in a positive way).
I wouldn't use this expression with people I don't know or I just met, however, as it implies for me a certain regularity of interactions with the person.
Je te revaudrai ça, promis !
Merci. Je vous revaudrai cela sous peu.
... à moins que le locuteur ne cherche à prendre sa revanche !
In addition to the other answers one could also say:
"J'espère pouvoir vous rendre la politesse"
Which reminds more of the original word, kindness.
I saw two sort of answers that cover the good posibilities for me (as a French guy):
J'espère pouvoir te rendre la pareille.
J'espère pouvoir te renvoyer l'ascenseur. (= I hope I can send you back the elevator)
À charge de revanche !
I think the specifics haven't been pointed out: the first solutions are more serious: if someone helped you when you had serious problems in your life, if someone asked a friend to prefer you for a job.
The second is way more casual, and can be said for example when someone paid for the restaurant. It can also be said by the giver to imply that next time, your friend is paying.
"J'espère pouvoir te/vous rendre la pareille"
Or, more casually:
"J'espère pouvoir te/vous renvoyer l'ascenseur"
While other answers are correct, I believe that the most academic way to express the idea of a debt towards a person would involve "redevable".
In Larousse dictionary, "redevable" has two definitions, the first for monetary debt, and the second for a more general meaning : "Qui doit un avantage, une faveur ou, ironiquement, un désavantage à quelqu'un".
As shown by Linguee, "redevable" is often used in political discussions at the European Parliament to express gratitude. For example:
Je vous suis redevable, ainsi qu'aux membres de cette Assemblée, des nombreuses remarques intéressantes qui ont été faites sur le fond.