What were the areas/regions of Europe that remained faithful to the Catholic Church?
The religious map of Europe has changed remarkably little since the Reformation. To a large extent, the confessional allegiances of European states today reflect the principle of cuius regio eius religio ("whose realm, his religion," meaning that a nation's ruler gets to decide its religion) established by the Peace of Augsburg in 1555. In order to bring an end to the destructive, bitter conflicts unleashed by the Reformation, it became necessary to allow the rulers of each territory to determine which religion their subjects should follow.
Catholicism remains the denomination of the vast majority of Italians, which isn't surprising given that Rome is the spiritual heart of the Roman Catholic religion. Though a strongly secular state, most Christians in France are Catholic, as indeed are those over the border in Spain as well as their neighbors in Portugal. Germany is a mainly a Protestant country, largely on account of its leading role in the Reformation. However, large swathes of the country, mainly in the South and West, are strongly Catholic, especially Bavaria. Over the Southern German border, Austria is also a Catholic country. Switzerland, the birthplace of the Swiss Reformed Church, is relatively mixed in terms of religious observance, though officially there are more Catholics than Protestants.
Croatia is Catholic, in contrast to its Orthodox neighbors in Serbia. Northern Europe is predominantly Protestant, but the Republic of Ireland is overwhelmingly Catholic, as are Belgium, Luxembourg and the micro-state of Lichtenstein. Many of the countries of the old Eastern Bloc are either Catholic or have large Catholic populations. These include the Czech Republic, Slovakia, Hungary, and Lithuania.
The answer to this question depends to some degree on how long after the Protestant Reformation you are asking about. For example, England remained faithful to the Catholic Church at first, but then broke away some twenty years later. Scotland remained Catholic for some time after England broke away but later became a bastion of Calvinism.
Generally speaking, the largest countries to remain in the Catholic Church were Spain and France. Both of these countries (as well as Portugal) remained mostly Catholic. Various parts of Germany remained Catholic as well under the rule where each ruler (there were many little states in Germany in those days) got to decide which religion his people would follow.
I am assuming this question is regarding the The Reformation?
The countries that remained predominantly Catholic after the typical time periods discussed when studying The Reformation (Martin Luther - Ninety-Five Theses 1517, Henry VIII and the establishment of the Anglican Church of England - 1534 and the resulting Catholic Reformation and The Council of Trent - 1545 - 1563) were Italy, Spain, Portugal, France, Belgium, Ireland, southern Germany, Austria, Poland and Hungary.