I believe changing one's voice and speech pattern to speak to a baby is a universal phenomenon. We certainly do in French. One common way to do it is to repeat a syllable. A few "baby" words, with the adult word in parentheses if it came from it:
sleep = dodo (dormir)
milk = lolo (lait)
train = tchoutchou (pronounced like "choochoo")
dog = toutou
teddy bear = nounours (ours)
The syllable repetition is a frequent pattern in French, not just in baby talk (for instance, it's a common way of making nicknames : Christian(e) --> Cricri ; Louis(e) --> Loulou, Albert --> Bébert, etc) but it works particularly well with babies.