All airlines I know of use the following boarding process:
First, let priority passengers board. This may include (either as a single group, or as several distinct groups):
- People with disabilities or requiring special assistance
- People with babies
- Premium class passengers (Business, First, Premium...)
- Premium fare passengers (Flexible fares as opposed to standard, discount, or light fares)
- Frequent flyers with status
- Passengers who paid extra for priority boarding, possibly by choosing "premium" seats (front seats, "extra legroom" seats...)
Then all the rest of the passengers using one of these methods:
- Most commonly back to front, especially on larger aircraft
- Sometimes window to aisle or other weird experiments like odd/even rows
- By priority groups based on check-in order
- Or just by queue order: first in line, first on board.
- In some cases, boarding will be split by rows between multiple aircraft doors.
Note that for some airlines, the procedure may vary depending on the flight (or actually the aircraft type), how full it is, the airport, and/or how much time they have.
Note also that in many cases, "back to front" will result in only two or three groups depending on the size of the aircraft, so you should still try to be first in line for your group to be sure.
I've never heard of an airline boarding "front to back", once you take aside priority groups. Some people in those groups are indeed at the front, but it's more a matter of how much they paid that the actual row they selected.
If you do not qualify for any of the priority groups, then depending on the airline, to board first:
- Check if there are any options to get priority boarding. Sadly, it seems at Icelandair the only options for that are to travel in the Saga Premium class
- Pick a seat towards the back of the aircraft (or for airlines doing window-to-aisle, a window seat)
- Check-in as early as possible
- Be first in line for boarding
Note that if the reason you want to board early is to avoid waiting for your luggage at baggage claim at the destination, don't forget you'll have to go through immigration first, and being at the back of the plane usually means you'll be among the last to disembark, you'll have a longer line at immigration, and checked bags will likely already have been delivered when you get to baggage claim (unless you land at CDG of course).
If you are in a hurry, it is often a much better idea to book at the front, and be first in line for your group. You are likely to still have space, and you will be among the first out of the plane, through immigration, and out of the airport.
Note that JFK-REK seems to be operating using 767-300ERs (you would have to check for your specific dates), and those of Icelandair at least seem to have relatively large overhead bins, and given their layout and number, it would probably be quite rare that all of them would be full. Also, longer, international flights tend to see people having more checked luggage and less carry-on luggage, not sure if that trend changed with the introduction of the cheaper no-checked-luggage-included fares.