There are two ways to look at sounds in a language. One is in terms of the higher-level abstraction the "phoneme", which refers to the system of differences, for example in English /p/ is different from /b/, and /p/ is different from /t/, but /p/ is not different from /pʰ/ nor from /p̚/. All of the phonemes of French are in French, and are not in English, and vice versa. The
"phonemes of a language" exist only in that language.
The second is in terms of physical realization. In English there are a number of differences in realization of /p/. The International Phonetic Alphabet is one scheme devised to allow us to talk about sameness at the physical level, so that we could talk of English as having physical [pʰ p p̚] – "allophones" (of the phoneme /p/). Even then, [pʰ] in English is not physically the same as [pʰ] in Hindi.
The French spelling [é] vs. [è] is an orthographic device that roughly conveys the phonetic difference defined in IPA as [e] versus [ɛ], but as in most cross-linguistic phonetic comparisons, the things covered by such a phonemic distinction are only roughly comparable. The phonological status of the vowel pairs is completely different in the two languages, and the physical pronunciation is very different. Of course, both French and English are sociolinguistically big languages, and one cannot get away with talking about "English" and "French" given the many dialects that exist. In some dialects of English (not my dialect), "gate" has a vowel very similar to Parisian [é], and "get" has a vowel very similar to Parisian [è]. In my dialect, the English vowels are more like [ɛi] and [ɛ].
In other words, the only sense in which the Parisian French vowels "exist" in English is that some dialects (spoken in the north) have similarly-pronounced vowels. But not identically-pronounced.