Who is the only player to have won the English Premiership title,
English FA Cup, European Champions Cup [this is the old name for the
Champions League - I'm unsure if the player won it as the Champions
Cup or Champions League] and the World Cup in his career and what is
his nationality?

Bobby Charlton 
Born: 11 October, 1937. Ashington, England 
 
International Caps  106  
International Goals  49  
Teams  Manchester United, Preston North End  
Team Honours  World Cup (1966)
European Cup (1968)
FA Cup (1963)
League Division 1 (1957, 65, 67)  

I am not a soccer fan but would League Division 1 and English
Premiership be the same...if so, this fellow meets your requirements.

League 1 is the old name for Premiership before the leagues were
restructured in the early 90's.

92/93 was the first Premiership season.  I understand this player has
to have won the Premiership title - and not the old Division 1.  
Also, the European Champions Cup has a good chance of referring to the
Champions League - as that was formed in 1992/1993 as well.

Did some more searching by drilling down from World Cup winners backwards:

You might be looking for 
Emmanuel Petit
17 | Midfielder
Height: 1.85m.   Weight: 75.00kg.   Nationality: France 
Born: 22/09/1970 in Dieppe  
First professional match: Monaco - Sochaux : 2-1 on 18/03/1989 

1998 World Cup winner (France)
2000 European Championship winner (France)
1997 French 1st Division Champions (Monaco)
1998 Premiership Champions (Arsenal)
1991 French Cup winner (Monaco)
1998 FA Cup winner (Arsenal)
1992 Finaliste of la Cup Winners Cup (Monaco)
2000 UEFA Cup Finals (Arsenal)
1989 French Cup Finals (Monaco)
2002 FA Cup Finals (Chelsea)

This seems to fit the bill.

I DON'T know if he is the only one but we have all the elements you
required with a Premiership in Arsenal/ An FA cup with Arsenal/ A Euro
Cup Champion with France and a World Cup with France.

Hope this helps.

Hello...

Unfortunately, it's not the European Championship that is needed -
it's the European Champions Cup now known as the Champions League.

The competition that was won this year by Liverpool.

Nicolas Anelka,

won the premiership and fa cup with arsenal in the 97/98 season. won
the world cup that year too with france. won the champions league when
he went to real madrid.

hope that helps