Œ, œ, like in œuf (egg) or cœur (heart), œuvre (multiple translations and meanings so I won’t detail here, it doesn’t matter), etc.
Æ, æ, like in nævus (the scientific term for mole (the dot on the skin, not the animal) or others.
æ is rarely used (I think it’s always scientific/medical terms from Latin?), but œ, however, is quite present in the French language.
Sadly, these special characters aren’t present on the French keyboard layout and a lot of people simply write “oe” or “ae” instead.
But some users have custom layouts, and autocorrection from smartphones, or some other writing help systems often automatically correct the words using the proper “merged characters”, like “oeuvre” → “œuvre”.
Currently, the search processes “oe” and “œ” as different strings, which leads to different results that should be common instead.