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In hebrew and arabic, the number 7 is "sheva" and "sabah" respectively, and the number six is "shesh" and "sita" respectively. These numbers sound very similar to their translations in some Indo-European languages:
7:
English: seven
French: sept
6:
English: six
French: six
Is there a reason for this occurrence or is it just a coincidence?
It's very possibly not a coincidence, actually. The numeral '7' is one of our best candidates for a Semitic loanword in Proto-Indo-European. Several of the PIE numerals are possibly loanwords from other families, including Semitic and some Caucasian languages. The PIE word septm̥, whence English 'seven', is possibly related to Proto-Semitic sabʕatum, the masculine form of the numeral 7. The PIE form still shows the Semitic collective suffix -t-, and the nominative ending -um. There are a number of other words which are possible candidates for Semitic loans in PIE; see the answer here for more.
The Semitic forms you reference in the question, sheva (Hebrew) and sabʕ (Arabic), are actually descended from the Proto-Semitic feminine, *sabʕum. It'd be more accurate to say that the masculine counterparts of these words are related to English 'seven', i.e. shiv'a (Hebrew) and sabʕa (Arabic).
It's been proposed that the PIE root for '6', *swéḱs, whence 'six', is also loan from Semitic, but I find this one less plausible; the PS is *t͡sidθatum or *sidθatum (whence Hebrew masculine shisha, Arabic masculine sitta). The phonetic similarity is a lot less evident, and the PIE form does not reflect collective *-t- or nominative *-um, unlike PIE *septm̥ : PS *sabʕatum.
