Inverter Question

compressor should be fine

as long as it doesn't have any fancy schmancy electronic control circuitry.

A compressor can draw a bit turning on.

check the max draw on the compressor motor they can pull alot of current when they kick on and see if it looks like your inverter can provide it.
you should not need a sine wave unit. I would give it a test run if the specs look ok and see if it runs ok or if you might need to rent something else

Finally moved this to the DIY area, which I should have done when it first got asked... Nothing wrong with the question, but it's more appropriate and I think you'd get better / more answers in the DIY space...

Gooserider

My French is horrid.
My misspleeled and typoed anglais will have to do.

Modified sine wave may cause damage to a newer compressor - typically in more high-end travel fridges, like the 'multi-fuel' that they sell to put in campers. That said, I have a cheapie Harbor Freight MSW inverter pushing an old dorm fridge in the camper I use from the in-laws, it's fine. Be sure to get one rated at the fridges max draw + 25% - a watt meter (like the Kill-A-Watt) is an invaluable tool for this. After you get it installed, you'll wonder where all your batterty life went, fair warning...

Ma Francais, c'est ne pas tres bonne, aussi.