You may want to work with the printer - most of the canvas printing sites I just googled recommend ridiculously low minimum resolution for larger prints. Canvas prints generally will not require as many PPI as a gloss or fine art print. Also, the printer will probably have software to up-res the art if it is not high enough in pixel count. In that case, work with them to print a small portion of your image with details and continuous tone (like a gradient from a sky or sunset) at the full, final resolution and inspect that small print yourself to see just how you camera's native resolution prints in that printer's workflow.
The 5DIII has a native output res of 5760 x 3840 pixels. At 72 inches, the native 5DIII image will yield 80 pixels per inch of print (5760 px/ 72 in). The canvas printing sites I was looking at were asking for as low as 60 PPI as a minimum so you may be ok. Again, work with the printer.
After up-resing, it may be useful to add a very slight amount of grain to break up the appearance of interpolated pixels - this might help the image appear more natural.
If you cropped your native file, then obviously you are starting with fewer pixels and you may need to judiciously up-res. You can do this in PS, but if you want an excuse to buy the latest AI-based up-resing software, have fun! Depending on the content of your image, you may find a lot of artifacts for the AI algorithms, so print small crops at 100% of the final resolution as hard proofs before paying for, and delivering, a huge print that looks terrible.
Have fun!
Kirk