The French tax on property is a bit weird (at least to us anglo-saxons). There is a simplified version whereby you can take a flat percentage of the income of the property as "expenses." The exact percentage depends on the type of property. But you always have the option of taking "actual" expenses, though I'm not certain how the mortgage figures into that, if at all.

Normally, the mortgage isn't an "expense" of the property when you rent it out - but depreciation is. It might be worthwhile to talk to a property agent in the UK to see what they would charge to handle all the "administrative" side of renting out your flat while you're gone and simply giving you a statement itemizing all the expenses of the property each year.
Cheers,
Bev