Considering that languages evolved just as species did complying with Darwin Natural Selection, what are the Genotype and phenotype when it comes to languages?
The assumption that language evolution is in any way analogous to darwinian species evolution seems to me to be completely incorrect. Here are two among the major differences:
1) Species evolution is driven by differential rate of reproductive success between individuals, themselves dependent of differential heritable traits. Languages evolution does not function in this way at all, with differential rate of reproductive success probably ill-defined. Even if it were, it would be correlated to socio-historical phenomena and presumably not at all to heritable characteristics of languages. It is the Roman legions, not Latin's case system, which spawned the Romance family.
and most importantly
2) One of the core logical concepts of (contemporary) darwinian species evolution is the distinction between heritable and non-heritable traits; only the former contributing to evolution. In fact, the very premises on which your question is built require this concept; otherwise there is no meaningful distinction between genotype (the material encoding heritable traits) and phenotype (actual expressed observable characteristic of an individual). However, language acquired traits are of course heritable: if a language looses the masculine/feminine distinction in the course of its history, for instance, it is very likely that many of its offsprings will also lack this distinction.
So I think it extremely unlikely that languages could have traits in their purported genotype which are not in their phenotype (so heritable traits with no observable expression) or conversely traits in their phenotype which are not in their genotype (so observable traits which are nonetheless not heritable). Or in other words, I doubt that the genotype-phenotype distinction makes any sense for languages.
Your question as an interesting spin-off though: once understood that language evolution does not obey the rules of darwinian species evolution, one could wonder which formal rules it does obey. Heritability of acquired traits would be there maybe alongside drive to simplicity (because of the acquisition of languages by infants) and some interactions with phonology and morpho-syntax (inflectional systems probably cannot survive high rates of syncretism, for instance).
I also do not think language evolution can be Darwinian. But I am quite willing to believe that human language has a biological basis and that possession of language has been a survival characteristic for us humans. The problem with assuming that natural selection has been at work is that we can't tell any difference among the various human languages in how they might aid survival. For social communication, they all work great. If all human languages aid survival equally, then natural selection cannot have played a part in aiding the survival of some at the cost of others.
This question makes more sense if it is altered slightly. Sebastian Shaumyan used the term linguistic genotype in his work on Applicative Universal Grammar to refer to a simplistic sign system that is heritable in humans and common in all human languages. The particular languages, English, French, Japanese, etc. and their vocabularies would be the phenotypes. This is Chomsky's idea of the Universal Grammar. It can be observed in the fact that if you adopt a chimpanzee, name it Nim Chimpsky, and raise it as a human it will not learn to speak a human language. However if a Chinese family raises an English child it can learn to speak Chinese. A chimp can relate symbols to meaning, like the sign for banana to an actual banana. But a chimp cannot make relations between signs in a sensible and consistent manner.
So although, it doesn't make sense to talk about the genotypes of a language because a language doesn't have the DNA to encode them in, we could talk about the linguistic genotype in humans.
As for jlawer's comment that is no genotypic basis to language, I would be interested in seeing how he draws this conclusion.