Well there were a few sword bearing Popes strolling around and a few more sword bearing Archbishops. Warrior Bishops were actually not uncommon for early medieval era either. The Medieval Church was quite different from the modern Church. As I said in 1100s it wasn't uncommon to have Archbishops that were married and had children. Normally 2nd and 3rd sons but sometimes if the eldest son died an Archbishop could still inherit and progress the family name and power at least into the 1500s though it became much rarer as time went on and traditions established more widely.
If you haven't read these yet they might be interesting for you-
http://en.wikipedia.org/wiki/Peerage_of_France
http://en.wikipedia.org/wiki/List_of_French_peerages
http://en.wikipedia.org/wiki/Aubrey,...ishop_of_Reims
http://en.wikipedia.org/wiki/Count
As you can see just from wiki that many Counts also held the title of Bishop- the harsh divide between lay titles and clergy was not so definite at this point though a Church title was normally considered more privileged than an equal ranked lay title many of the high nobility also carried Church titles as a shield against the demands of vassalage. They could always claim their first duty was to the Church and the Church gained power by playing off the lower nobles against the Dukes and the King. Eventually more and more King either took the power of the Church onto themselves (investiture controversy in HRE, King of England becoming head of the Church, etc) or ensured that the divide between lay titles and Church titles was clear so that the clergy answered to the Pope and the lay vassals answered to the King.
Not as many that were named Archbishop would be active politically outside the Church or also be generals but there were a few. It was much more common for Bishops and lower orders. That is why I proposed that the title of Archbishop also have lowered command so rarely should they be leading armies but they could call men to arms and give the strategic orders that an army would follow while tactical command would be assumed by someone else.
If you read more beyond the Wiki you can see how often the politics of the Church and the nobility were often shared since most of the nobility were also the high officials in the Church. Though the later Church had a bit of a meritocracy where lower ranked people had some chance at progression it still was rare that any other than noble born was elected higher than Bishop.
As for Flanders... I think Bruges and Ghent are enough in 1100. Brussels did become quite important in the 1300s but that is 200 years after the start date we are talking of. The distinction between upper and lower is probably a good thing to keep in mind however with lower being more Flemish and upper being more German.