I have a water report from Belgium in which (literal translation):
total hardness calculated = 18.4 French degrees
temporary hardness calculated = 11.4 French degrees
bicarbonates calculated (equilibrium) = mg/l HCO3 138
Given that 1 French degree = 10 ppm CaCO3 I conclude that the bicarbonate number is based upon temporary hardness and not total hardness.
I thought bicarbonates are calculated from total hardness. Am I wrong?
No! Bicarbonate content is a factor in calculating Alkalinity. Alkalinity is almost always equivalent to Temporary Hardness. Therefore, the bicarbonate content should be calculated from the Temporary Hardness.
I think I confused total alkalinity and total hardness, right? 
You did confuse them, but there is still uncertainty as to what your water’s alkalinity actually is.
As I mention, Temporary Hardness is USUALLY equivalent to the alkalinity. But a water source could have high alkalinity and low hardness. Witness a case where you add sodium bicarbonate to distilled water. That water has zero hardness, but it certainly has alkalinity from the added bicarbonate. Some water sources could be similar to this. Thus, its not always true that Temporary Hardness is equivalent to Alkalinity.
Thanks for the explanation. One more question, if I may: if the water company only gives you hardness expressed in French degrees, is it possible to derive total alkalinity from that number? I know the relationship between French degrees and ppm CaCO3, obviously.
Nm, it’s not really possible afaik. Emailed the water company to get the HCO3 values.