The French elect their president by direct national popular vote - and when the president's party also controls the French parliament, he's a pretty powerful man. (When it doesn't, he's not - their system is interesting that way, in most other countries the respective powers of president and PM, assuming both functions exist, are well-delineated and clear regardless of which party holds which.)

Of course, the French election system does have two rounds (if no candidate gets 50% of the vote in the first round, there's a second round between the two candidates with the most votes), which can backfire spectacularly like in 2002 when the far-right candidate snuck into the second round, the socialist candidate having lost too many votes to the various communist parties (yes, France has multiple communist parties...). Chirac got a record landslide victory in the second round as a result, but it was hardly something to be proud of. In short, not exactly a system anyone would want to imitate.

I'm rather puzzled by your comment about the British Speaker of the House being President... what did you mean by that?