>Ê with the circumflex accent marks an “e” after which originally some other letter was written (usually an S), but this letter is no longer present in its modern spelling.

[snip]

>By imagining “es” instead of “ê”, we can often deduce the meaning of unknown words; for example, forêt = forest, fête = “feste” = fest(ival); intérêt = interest and many others. The circumflex accent is used in the very same sense also for other vowels, for example île = isle, hôte = “hoste” = host, hâte = haste.

I will always remember this, thanks to my high school French teacher who, knowing her audience, gave us a few examples like "hôpital," and then said "So you can probably guess was 'bâtard' means..."