There is a tendency in some of Romance and Germanic for historical vowel length to be associated with open-mid / close-mid or tense / lax distinctions, and vowel length is cross-linguistically correlated with syllable structure (short if closed). (This paper addresses "loi de position" and assembles a possibly complete list of cases of such a correlation in allophony). Even in French, it is not limited to the open-close distinction, since Laurentian French has also developed [i/ɪ; u/ʊ] correlated with syllable structure.
Looking across language in general, there does not seem to be any documented tendency in that direction. Usually, the distinction between e/ɛ, o/ɔ or i/ɪ, u/ʊ is attributed to a feature ATR, except in Romance and Germanic. In the many languages with an ATR distinction, there is no tendency for ATR contrasts to be dependent on syllable closure. However, languages with reported e/ɛ, o/ɔ, i/ɪ, u/ʊ contrasts are not all that common outside the ATR set (diagnosed by vowel harmony), so it is hard to tell if there is a significant trend within that set of languages.