Is that loose of a search not actually desirable in "find in page" instances?
In other words, are there many words where 'e' matching 'é' would actually generate a false positive? This is the only case I could see that would be problematic.
And even then "find in page" is usually used as quick navigation to the minimum matching search (high recall) and not about excluding all possible mismatches (high precision).
It's even worse than that. 'e' is the most used letter in french, but 'é' and 'è' are quite used too. 'ê' and 'ë' being rarer, but still existing.
So, I am exaggerating it a bit, but you can compare it to having to search for words with the consonants, because every vowel is considered the same by your search algorithm.
Yes, I'm pushing it, but you see the problem it can easily become in huge pages.
Most pages nowadays are small enough that it won't be a bother, but their still are some cases (newspaper posts, blog analysis, etc...) where accent sensitiveness will be an issue.