Chanceux vs. heureux

In French, the words 'chanceux' and 'heureux' can both convey a sense related to luck, but they are used in subtly different ways.

Chanceux

'Chanceux' translates directly to 'lucky' and is used specifically to describe someone or something that has had good luck, often by chance rather than through their own actions.
Il est vraiment chanceux d'avoir trouvé un billet de vingt euros par terre.
(He is really lucky to have found a twenty-euro bill on the ground.)
Elle a été choisie pour participer à l'émission de télévision; quelle chanceuse !
(She was chosen to participate in the TV show; what a lucky person!)
Gagner à la loterie est signe qu'on est vraiment chanceux.
(Winning the lottery is a sign that one is truly lucky.)

Heureux

'Heureux', while it can mean 'happy', also implies being fortunate or blessed, often with a sense of satisfaction or contentment derived from favorable circumstances. It can also refer to luck in games of chance or gambling.
Ils sont heureux d'avoir trois enfants en bonne santé.
(They are fortunate to have three healthy children.)
Après avoir entendu les bonnes nouvelles, je me sens vraiment heureux.
(After hearing the good news, I feel truly fortunate.)
J'ai été l'heureux propriétaire du billet de loterie gagnant.
(I was the lucky owner of the winning lottery ticket.)

Summary

'Chanceux' and 'heureux' both convey elements of luck, but with nuanced differences. 'Chanceux' refers to good fortune resulting from chance, whereas 'heureux' implies a sense of gratitude or satisfaction with one's circumstances. Although they can sometimes be used interchangeably in casual conversation, an awareness of their subtle differences will allow them to be expressed in French in a more precise and evocative way.