I'm not really prepared to provide a break down of the demographics of Europe vs. Syria so I can't address that part of the question. I can however discuss the reasons for the successes of the First Crusade, which seems to be the main target of your question. The later Crusades are very different from the first and so would require a separate post.

For the sake of simplicity I'm going to outline the main advantages that the First Crusade had for its success. I can probably add extra information on each one if you're interested in more. The issue with the term Franks has already been better addressed in another post and I'm assuming you meant the Crusaders in general rather than the French knights in particular.

1 The Muslim world was a mess of internal conflicts and infighting.

If we take the simplest view the Muslim world was split in two between the Fatimid Caliphate in Egypt and the Abbasid Caliphate in Baghdad. The Fatimids were Shiite and the Abbasids were Sunni. Syria was far enough from Baghdad that the Abbasids only had moderate to minor influence in the area while the Fatimids were trying to expand their area of control. The Fatimids even took Jerusalem while the Crusaders were marching south through Syria. While this theological split was on the top levels of society there was also a lack of unity between the nobility, if we want to use that term, in the area. There was a distinct lack of trust between Muslim commanders that prevented them from uniting to oppose the Crusading army. The largest force they formed to deal with the Cruaders, led by Kerbogha at the city of Antioch, actually fell apart when the Crusaders attacked in a large part due to a lot of commanders not caring if Kerbogha was successful or even wanting to see him fail so they could benefit from his downfall. It seems largely that they didn't see the Crusaders as a theological foe, instead they were another element of the regions politics to be ignored or used like any other.

2 The Crusaders were better armed.

'Better' is a very subjective term so it probably isn't really accurate here. They wore heavier armour and were better equipped for the types of battles they ended up fighting. The local Turks and Arabs struggled to reliably penetrate the Crusaders mail armour while he heavier European weapons did not face a similar problem when it came to Muslim boiled leather. Most of the battles of the First Crusade were resolved by the Crusaders charging the Muslim army and either driving it off or killing them. That said, the campaign was marked more by major sieges than battles.

The actual reasons for the First Crusade is obviously a lot more complex but those two factors, especially the first, helped them succeed. On the topic of sieges while Syria was full of fortresses the Crusaders actually bypassed rather staggering numbers of them. While the most iconic moments of the Crusade are probably the sieges, especially Antioch and Jerusalem, they simply ignored a lot of the fortresses between Antioch and Jerusalem. The aforementioned lack of unity among the Muslim lords made this possible since many of those in charge of the fortresses were happy to let the Crusaders pass without bothering them. At the major sieges the Crusaders undertook they showed their experience and skill at taking major fortresses. Antioch was taken thanks in no small part to treachery from a Christian Armenian in the fortress while for Jerusalem they built Siege Towers to take the walls with. Say this for the Crusaders, they knew how to commit to a siege and were not easily discouraged.

I don't know enough about Middle Eastern fortifications to comment on the quality of them compared to contemporary European castles. I will note that many of the most impressive castles in the region now, however, were built by the Crusaders.

Thomas Asbridge's The Crusades is probably my favorite general history on the subject. He also wrote a history of just the First Crusade but I haven't read it. Jonathan Riley-Smith's The Crusades: A Short History is also a great book.

The Franks are generally considered distinct from the French. The Franks were from a collection of territories inhabited by Germanic tribes and consolidated first under the Merovingians, then under the Carolingians. When the Carolingian Empire fell apart, so too did Francia as it stood, where it was replaced with the Capetian dynasty that started out ruling the area immediately surrounding the Ile de France. It is at this point that many historians begin calling these people "the French," for lack of a better term. Thus, the Franks weren't involved in the crusades at all, because no Frankish kingdom existed in 1095 when Urban II called for the first crusade, but the French were. Now, some chronicles will call the French the Franks by mistake, but they are indeed different (someone with better knowledge of French chronicles can expand on this for me).

To your point, however, assuming that you meant the French were successful, the history of the crusades was not a rousing success for the Christians by any means. A good place to start your reading on the subject would be a general volume by Jonathan Riley-Smith, one of the foremost experts in the field, who has published a number of books on the crusades.