It is so probable that all Caucasoid people have had a common ancestor. Does The fact that most of Caucasoid people speak a Semitic or Indo-European language not suggest that there has been an ancient language sometime in the past that primitive Caucasoids spoke it and from which these groups have been derived?
Language and genetics, as much as they tend to correlate, don't necessarily have to at all. People can, and do, frequently adopt languages that have no connection at all to their own ancestry. It may well be the case (and probably is) that something like this has happened in the case of Indo-European and Semitic.
I'm not sure exactly what you mean by 'caucasoid' (and I'm not sure that your knowledge of human genetic history is very accurate), but certainly there are a couple of clear counterexamples for you. Basque is the most obvious - clearly not Indo-European, and indeed clearly pre-Indo-European, and yet spoken by people that are genetically very European. Sumerian and maybe Elamite might have also been counterexamples - they've since been replaced by Semitic languages (> Aramaic > Arabic in the case of Sumerian) or Indo-European languages ( > Persian in the case of Elamite), despite the fact that neither language was anything like either Semitic or Indo-European (or each other) and the fact that the people that spoke them were never 'replaced' with anyone else.
Indo-European languages are more closely related to Altaic (including Turkic, Mongolic, Japanese, Korean), Eskimo-Aleut, Chukotko-Kamchatkan than Semitic. The most of speakers of those language families belong to Mongoloid race. It is thus difficult to infer any relation between race and language based on this fact.
On the other hand, the speakers of, say, Chinese while belonging to Mongoloid race, speak a language which is much further from Indo-European than Semitic.
While we can more or less reliably speculate that the speakers of Proto-Indo-European were Europeoid, we cannot do any conclusions of similar reliability about Eurasiatic or Nostratic.