Difficult to know the exact meaning without knowing the exact language it is form, and how it was spelt there. But, it almost definitely has only the bit `the feet' in it, no goddess (though it may have a feminine suffix), nor viSNu. cara is an old word denoting movement (cognate with -τολη- and -πολο-), and caraNa is the thing one moves with, i.e. the feet. The symbolism of falling and holding someone's feet to ask for protection is an old one, and so is the idea that an inferior (as human is to divine, or peasant is to king) casts his eyes downward at his superior's feet.
It is a common concept to name a child as being at the feet of some divine being.