While eventually and éventuellement both refer a hypothetical event, the occurrence they allude to takes place in one part of the space-time continuum in English, and another in French. Calling Dr Who to the rescue!
As devotees of the long-running TV series know, the Doctor travels both in time and between worlds in the Tardis, a time-machine/spaceship disguised as a police box. Read on to find out how science-fiction can help us distinguish this week's false friends.
Let's start with the sentence: If you work hard, you will eventually succeed.
The hypothetical event (you will succeed) occurs at some point in the distant future - we're talking time travel here! In this example, eventually can be replaced with in the end, in due course, by and by, sooner or later, in time. This indicates that when translating into French the correct choice is a time expression such as un jour, tôt ou tard, à terme:
Si vous travaillez dur, un jour ou l'autre vous réussirez.
In contrast, éventuellement indicates that the event is in the realm of possibility, without any indication of when it might occur:
Vous pouvez éventuellement prétendre à 30 jours de congé parental supplémentaires.
The hypothetical that this example refers to is clearly a parallel world – one that happens to look like Scandinavia... The idea is often best rendered in English by may or might:
You may be eligible for an additional 30 days of parental leave.
Depending on the sentence structure and the degree of likelihood you need to convey, you could also use maybe, perhaps, possibly, hypothetically or probably.
So, remember: time machine in English, spaceship in French!