Can I use an F-test to test the equality of variances if my distribution is leptokurtic? 
I have the data for two leptokurtic distributions. I want to use the f-test of equality of variances but as I understand it needs to satisfy the assumption that 'the two populations are normally distributed'. Is a leptokurtic distribution still considered as normally distributed? Can I still apply an f-test?
Thanks.
 A: 
Can I use an F-test to test the equality of variances if my distribution is leptokurtic?

Quite clearly one can do so, much as one can attempt to shave with an electric knife. 
There's a bigger question of whether it's wise to do so.

I have the data for two leptokurtic distributions. I want to use the f-test of equality of variances 

Why do you want to use the f-test for this?
Why do you want to perform a hypothesis test for this at all? What problem are you trying to solve?

but as I understand it needs to satisfy the assumption that 'the two populations are normally distributed'.

If you want the test statistic to have the usual desirable properties (significance level close to the one you ask for, reasonable power), then it needs to be very close to normal.
Consider a distribution which looks very similar to yours (sample histogram below):

-- simulation indicates that the distribution of p-values under the null for this distribution is very much skewed toward small values. This means that when there's no difference in variance, the F-test is very likely to reject. My simulation at n=100 in each of two samples put the true type I error rate for a 5% test at over 60%. Here's a histogram of p-values under the null hypothesis:

If the test was behaving reasonably, it would look close to uniform. This is not a desirable state of affairs.

Is a leptokurtic distribution still considered as normally distributed? 

Leptokurtic means 'having a higher kurtosis than the normal' (indeed, in this case, it seems distinctly higher). 
How could a distribution with higher kurtosis than the normal has be considered normal? 
If you mean "is it sufficiently close to normal to still use the test?" then the previous simulation would suggest that - at the least - you'd have to be very tolerant of a much higher than nominal rejection rate.

Can I still apply an f-test?

You can. I would caution against it.
If you would like to know of some alternative tests, you should probably ask about those (though some common ones are discussed in numerous answers here). More important, I think, is what you're hoping to achieve by testing at all.
