What rate of French tax will be applied to my rental income?

Under the Regime Réel any profits after allowable expenditure are taxed at a rate of 20%.

In addition profits are subject to Prelevements Sociaux of 17.2% (or 7.5% if you are subject to an EU or EEA member state national insurance legislation other than French, or subject to UK national insurance legislation under some conditions). 

Example 5.000 Euros of profit.

5.000 Euros @ 20% = 1.000 Euros + 5.000 Euros @ 7.5% = 375 Euros

Under the Regime Micro-Entreprise 70% of turnover (or 50% of turnover if the property has been awarded with a tourist classification) is deemed to be profit, with this being taxed at a rate of 20%.

In addition profits are subject to Prelevements Sociaux of 17.2% (or 7.5% if you are subject to an EU or EEA member state national insurance legislation other than French or subject to UK national insurance legislation under some conditions). 

Example 10.000 Euros of turnover gives a profit / taxable income of 7.000 Euros (10.000 * 70%)

7.000 Euros @ 20% = 1.400 Euros + 7.000 Euros @ 7.5% = 525 Euros