The French generally spoken in France does not have [ɪ] either phonemically or phonetically, and to my knowledge no variety of French would use it for the first vowel in « s'il vous plait » (though the /l/ often disappears, leaving a shorter first syllable).
To be clear — as you've since acknowledged — the terms "short" and "long" that we learn in elementary school in English are misleading when talking about vowels since they're not really related to length. So we can avoid that red herring of a path.
To round out the standard answer above, some varieties of French do have this sound. The one I know best is Canadian French, in which [ɪ] is one of a series of lax realizations of the high vowels.
These are the high vowels in French:
- /y/ : allophones [y] (only option in France) and lax [ʏ]
- /u/ : allophones [u] (only option in France) and lax [ʊ]
- /i/ : allophones [i] (only option in France) and lax [ɪ]
(Note that the exact realization varies by dialect. For [ɪ], I've heard [ɨ] and even a diphthong like [ɪj].)
These novel lax variants appear in closed syllables, i.e. syllables where the coda is filled by a consonant. Hence, you encounter paradigms like this:
citer [siˈte] ~ cite [sɪt]
lutter [lyˈte] ~ lutte [lʏt]
router [ʁuˈte] ~ route [ʁʊt]
According to Survenant's research in his answer, the contexts are even more limited: these lax variants only appear in closed final syllables. This isn't consonant with my own experience, but I bring it up in case I'm mistaken.
Where do these lax variants come from?
It's sometimes thought that [ɪ] arises in Canadian French because it occurs in English, and Canadian French is often accused of being influenced by English. This deserves a quick comment. While lexical, morphological, and syntactic borrowing across languages is common, phonetic borrowing is rare by comparison. Even heavy exposure to a non-native language rarely penetrates a person's phonetics; hence, accent often goes unmastered even by proficient learners.
Moreover, the influence of English would not account for [ʏ], which is not present in English; nor the distribution of [ɪ] and [ʊ] only in closed syllables, which is not the case in English; nor the existence of parallel changes in Belgian French, as mentioned by Greg.
Luckily, we have a better explanation for the appearance of these lax vowels. The pattern in which they show up actually exists in standard French. However, in standard French it only applies to the mid vowels, namely the pairs [o] ~ [ɔ], [e] ~ [ɛ], and [ø] ~ [œ]. By adding the set of high vowels, Canadian French extrapolates the pattern to new cases. This type of linguistic change is called "analogy", and it's relatively common. So this is a plausible hypothesis.2
1 A reasonable component of any answer about "French". If someone asked whether to pronounce /r/ at the end of a syllable in English, the answer would be "No in most British dialects, yes in most American dialects." If someone asked whether Christians baptize infants, the answer would be "Catholics do, most Protestants don't." Only by demoting one kind or the other could you reduce the answer to "yes" or "no", and from a descriptive linguistics point of view that's not an interesting exercise.
2 Incidentally, Canadian French is also distinguished by certain words with a final consonant absent in other varieties of French, including frette (< frais ?), litte (< lit), icitte (< ici), and toute where you'd expect tout. One could speculate about a symbiosis between this phenomenon and the extra lax vowels. If you create more contexts where a distinctive dialect feature appears, and this feature renders those contexts more salient, is that subconsciously leaning into your sociolinguistic identity?