>>> Then I think injecting LC_ALL=C into the environment when running Grep 
>>> in this case makes the results more useful?  And we can then avoid 
>>> using -a?
>>
>> I'm not so sure. LC_ALL=C seems more problematic than -a:
>>
>> $ grep ф test.txt
>> фыва
>> $ grep -a ф test.txt
>> фыва
>> $ LC_ALL=C grep ф test.txt
>> (nothing)
>
> I guess this regression in Grep happened when they "internationalized" 
> the DFA code, sigh...
>

FWIW, I "bisected" this with various versions of grep, and this regression 
happened in 2014, between versions 2.20 and 2.21:

echo -ne "premi\xE8re\n" > latin1.txt
echo -ne "premi\xC3\xA8re\n" > utf8.txt
echo -ne "premi\xE8re\npremi\xC3\xA8re\n" > both.txt

With 2.20 with rxvt (which is clever enough to display UTF-8 and Latin-1 at the same time):
$ grep prem *.txt
both.txt:première
both.txt:première
latin1.txt:première
utf8.txt:première

With 2.20 with M-x shell (the \350 is a single character):
both.txt:premi\350re
both.txt:première
latin1.txt:premi\350re
utf8.txt:première

With 2.21, with rxvt or M-x shell:
grep prem *.txt
Binary file both.txt matches
Binary file latin1.txt matches
utf8.txt:première