There is no "International" carry on size. Each airlines has its own rules. #YES, you should comply
HAND BAGGAGE DIMENSIONS
The maximum dimensions of your hand baggage are: 55 x 35 x 25 cm / 21.6 x 13.7 x 9.8 in. (including pockets, wheels, and handles).
YOUR HAND BAGGAGE WEIGHT
If you are traveling in the Economy cabin, your hand baggage and personal item cannot exceed 12 kg / 26.4 lb. If you're traveling in the Premium Economy, Business or La Première cabins, the combined weight of your hand baggage items and accessory must not exceed 18 kg / 40 lb. Your travel cabin is shown on your ticket.
Carry-On Size Restrictions
Combined length + width + height of baggage must not exceed 45 linear inches (114 cm)
Individual length, width and height measurements may not exceed 22” x 14” x 9” (56 cm x 35 cm x 23 cm) respectively
Carry-On Weight Restrictions
No maximum weight applies to carry-on baggage, except in the following locations.
Singapore, Beijing, China, Shanghai, China
Additionally you may bring a "Personal Item". Delta does not identify a size, but Air France does:
AUTHORIZED PERSONAL ITEMS
In addition to your hand baggage, you may bring 1 personal item. This item cannot be bigger than 40 x 30 x 15 cm / 15.7 x 11.8 x 5.8 in.*
You may bring:
or 1 bag for your computer, camera, or any other electronic device.
You must place your personal item in the seat in front of you, unless you are seated in an exit row. If you are seated in an exit row, your personal item must be stored in the overhead compartment.