It looks like inputFile has Windows-style line-breaks (CRLF) but your program is splitting the input on Unix-like line-breaks (LF), because std::getline(), breaks on \n by default, leaving the CR (\r) at the end of your string. 
You'll need to trim the extraneous \rs. Here is one way to do it, along with a small test:
#include <iostream>
#include <sstream>
#include <iomanip>
void remove_carriage_return(std::string& line)
{
    if (*line.rbegin() == '\r')
    {
        line.erase(line.length() - 1);
    }
}
void find_line_lengths(std::istream& inputFile, std::ostream& output)
{
    std::string currentLine;
    while (std::getline(inputFile, currentLine))
    {
        remove_carriage_return(currentLine);
        output
            << "The current line is "
            << currentLine.length()
            << " characters long and ends with '0x"
            << std::setw(2) << std::setfill('0') << std::hex
            << static_cast<int>(*currentLine.rbegin())
            << "'"
            << std::endl;
    }
}
int main()
{
    std::istringstream test_data(
        "\n"
        "1\n"
        "12\n"
        "123\n"
        "\r\n"
        "1\r\n"
        "12\r\n"
        "123\r\n"
        );
    find_line_lengths(test_data, std::cout);
}
Output:
The current line is 0 characters long and ends with '0x00'
The current line is 1 characters long and ends with '0x31'
The current line is 2 characters long and ends with '0x32'
The current line is 3 characters long and ends with '0x33'
The current line is 0 characters long and ends with '0x00'
The current line is 1 characters long and ends with '0x31'
The current line is 2 characters long and ends with '0x32'
The current line is 3 characters long and ends with '0x33'
Things to note:
- You don't need to test for EOF. 
std::getline() will return the stream, which will cast to false when it can read no more from inputFile. 
- You don't need to copy a string to determine its length.