Even the crying of newborn babies seems to be more musical than we think. This can be concluded from an interesting study that was published last month in Current Biology . German researchers were able to show that newborns don’t just cry randomly, but - when studying the audio signal of their crying - one can distinguish between French and German babies. The German babies - only three days old - cry in a downward fashion, their French contemporaries showed an increasing swelling of the cry and stop abruptly.
Sound example: German & French baby cries (Source: BBC).
How can we explain these differences? Babies do hear about three months before they are born. And the few prenatal studies that are available show that babies, in that stage of their development, already perceive and remember sounds. For instance, they recognize the sound of their mothers voice just after birth, and they can distinguish between tunes that they heard during pregnancy from those that they have never been exposed to before.
The correlation between the mother language of the babies and their average crying pattern, suggests that exposure to the language spoken by their caregivers (mother, father, etc.) influences the crying, since French language, on average, consists of raising melodies, and German intonation often shows a decreasing shape. The researchers suggest that this as a sign of a sensitivity to language from very early on in life.
My interpretation would be different. I would not so much relate these results to language, as well as a sign of a high sensitivity to the musical aspects of speech: rhythm, melody, stress (i.e. prosody). As quite some studies have shown (e.g., authors like Fernald, Trehub, Trainor, and others), infants and young children are extremely sensitive to these 'musical' variations in their environment. For example, infants seem to be highly sensitive for the musical and emotional aspects of infant-directed speech (IDS), more so than the actual linguistic structure, let alone semantics. I would therefore claim the results of the baby-study are actual evidence for very early signs of musical sensitivity to intonation and other musical aspects of sound, than that it should be seen as evidence for the start of learning a language.
 Mampe, B., Friederici, A., Christophe, A., & Wermke, K. (2009). Newborns’ Cry Melody Is Shaped by Their Native Language. Current Biology. DOI: 10.1016/j.cub.2009.09.064.