What happens when the current fed to a device is higher than the specified value?
The current drawn by a device (your fans) is a factor of that device's impedance. The current rating of a power source is the maximum current that source is capable of delivering or should  be allowed to deliver. 

Thus, your source having a higher current rating is not a problem, the fan will draw what it needs at the specific voltage expressed across the fan's contacts. 

If the solar panel is not able to deliver that much current at a given time, i.e. if the panel is shaded or the light source is weak, the fan will run slower or not at all, but no harm will come to either. 

You definitely do not need to split the current across two fans in parallel to consume all available current from the solar panel, what is not needed will simply not be delivered. 

The only mild concern from the question is the 5 Volt rating of the fans compared to the 6 Volt capacity of the solar panel: Realistically, a 5 Volt rated fan should work fine in this specific situation, because once the fan starts drawing current, the solar panel's voltage will drop due to its internal resistance. Motors (i.e. the fan) are pretty resilient to slightly higher than rated voltage as well.