There are 3 possible scenarios for coolant level sensor to go off; 1, there is air pocket in your cooling system, 2, faulty sensor, 3, actual leak.
As you mention that you do smell coolant burning tells me coolant may be leaking into oil due to faulty seal. In order to be sure ck your oil and oil cap to see if it present scummy residue on top of the oil cap and feel and smell oil to be sure.
If you smell inside the car, chances are your heater actuator would be leaking and you can ck that by peeling your carpeting on the driver side (U.S. models). Hope that won't be the case as it is a true PITA to work on.
If you don't have any symptoms listed above you may have a classic leak from T-stat neck (back of the neck) which is very hard to detect. And if that's the case replace your t-stat while you repair the leak.
Good luck and let us know how it turned out!
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