Instead of capturing each data element one at a time with separate
user.scan's, it's easier to create a match object from a single
regular expression that contains match groups.  You can then access
the results of the match group by using $1, $2, etc.
Try this:

Cemployee=Array.new
CemployeeID=Array.new
CemployeeName=Array.new
counter=0
CemployeeS=" "
File.open("D:\\finance.txt").each { |user|
  m = /^([C]\d+)\s(\w+,\s?\w+)/.match(user)
  if m
      CemployeeID[counter]=$1
      CemployeeName[counter]=$2
      puts "Name: #{CemployeeName[counter]} ID:
#{CemployeeID[counter]}"
      counter+=1
    end
}

Hope that helps-

Brian