Since this question was recently resurrected, I'd like to provide a broader perspective.
The problem is that the question of the evolution of language is often confused between three quite independent (although related) issues.
- What is the evolutionary selective advantage of language? Or what evolutionary purpose does language serve?
- What is the origin of language? What were the features that were first selected on? What was the first language like? What were the first phases of language like.
- What are the mechanisms by which language develops and changes?
There has rightly long been deep seated skepticism in linguistics about questions 1 and 2. It has only been quite recently (maybe last 20 years) that the questions of language evolution in the early stages have been considered to provide serious insights, mostly due to the use of models. However, there is no universally accepted answer to 1 and 2. There is not even universal agreement on whether language is a directly selected feature or an epiphenomenon of other kinds of natural selection resulting in the neural and anatomical features making language possible. It's also not clear whether the early stages of language were more holistic (larger units imbued with complex meanings becoming modern language through articulation and analysis) or very particular (small units with small meanings being synthesized into larger units). It's not even clear if language has a single origin. These questions can likely be never settled completely and often reflect the worldview and current philosophical leanings of their investigators more than comprehensive analysis of extensive evidence.
While the answers to questions 1 and 2 can only be speculative, there is vast literature documenting the answers to question 3. We know a lot about the mechanisms by which language changes at all levels. Phonetics to lexicon or syntax. The process of grammaticalization. The processes of Creolization. The various social aspects of prestige, code switching, and standardization. All of this knowledge is partial and there are no definitive predictive models. But we certainly know where to look for more data.
Looking at the wealth, depth and breadth of the evidence, it makes no sense to ask the fourth popular question. Is language change subject to the evolutionary processes of natural selection? Language (as it is now) is a phenomenon with a strong social dimension and therefore it makes no more (or less) sense to think of it as evolving by natural selection than it does any other social phenomenom (from fashion to war). While models inspired by various selectionist metaphors can certainly be illuminating (e.g. see Dixon's thesis of punctuated equilibria or even Dawkins' memes when applied to the lexicon), they are always very partial and break down when we try to universalize them.
Looking at the existing evidence and future research paradigm it is unlikely that language change needs the metaphor of natural selection to explain what's going on. This is partly because there's so much cultural (Lamarckian) selection involved and partly because the processes of encoding and transmission of the features on which selection could operate are relatively well-known and look nothing like the straightforward digital encoding present in the genes (even when we take the more recent environmental modifications into account). You could certainly look at some of the changing units of language (for instance words or salient phonological features) and study their 'reproductive' success. But that instantly transforms the feature you're studying into an organism and the whole metaphor becomes too circular to explain much of anything.
In short, while I wouldn't go as far as the 19th century French academics who forbade any discussion of language evolution, it is not a question very high on most linguists' minds. All the fundamental questions have been argued to death and few people think a resolution is in sight. Occasionally a fascinating hypothesis comes along that shines a light on other aspects of language (I was quite taken with Dunbar's work and found Dixon's arguments very fruitful), but ultimately it's not a fundamental question of modern linguistics. It sparks popular imagination and individual curiosity of many but we will most likely be left to ponder these dilemmas forever.