Why did the Ottoman Empire not industrialize or not reach the level of those nations?
The question is broad, and there's a laundry list of contributing factors that tie in together. (As you go through this list below, keep in mind that I probably missed many other factors.)
The biggest factor is that the Renaissance occurred in Europe. As did the Enlightenment, which introduced the notion of rule of law to boot. The answer I just linked to sketches out a number of reasons why that was with a few references that are good sources for this answer too.
An important point to keep in mind about the late Medieval and Early to Mid-Renaissance is that it was an industrious period from a scientific standpoint, and in many ways a period of agricultural revolution. The period saw developments such as the Three Field System, plowing-related technologies, mill-related technologies, etc. -- all of which contributed to significantly boost the agricultural output. This revolution wasn't as pronounced in the East Mediterranean basin, or at least slower -- which means there was less available labor. The period also saw the advent of universities and the printing press.
Speaking of the latter, on the scientific literacy front, the Printing press did its thing and spread wealths of new knowledge far and wide across Europe. In the Ottoman empire, by contrast, no book was officially published until into the 18th century.
And speaking of science, there was a Muslim attitude change towards the latter at some point between the 14th and the 16th century depending on which historian you ask. Whichever it is, it was in full swing by the mid- to late Renaissance. The Tarqi ad-Din observatory in Istanbul, for instance, was destroyed by a squad of Janissaries by order of the Sultan, on the recommendation of the Chief Mufti around 1577.
The next biggest factor was the circumnavigation of Africa and the discovery of America in the 15th century. Until those two events, the silk road, which went through Ottoman territory, was a key trade route and a source of tremendous wealth for the Ottomans. Bypassing it enabled Europeans to control world trade and accumulate enormous quantities of capital. New trade routes to the Spice Islands, India, China, and the New World enabled Europeans to build the financial backbone that enabled industrialization to begin with.
In passing, on the financial front, innovations out of Northern Italy and, a bit later, the Low Countries, introduced Hindu-Arab numerals, place value, double-entry bookkeeping, bond trading, early stock markets, and early economics.
Another major factor was societal. Side note here: You mention France industrializing, but actually it didn't as much or as fast as the UK or, later, Germany. The reasons are several. Part of it was Louis XIV kicking Protestants out, which benefitted Great Britain, the Low Countries, and Germany. Part of it was that French nobility, in stark contrast with its GB counterparts, basically wasn't allowed to earn money except from land rents.
With this side note in mind, there was some degree of societal inertia going on in the Ottoman Empire too. A group that deserves special mention, I would put forward, are the Janissaries. Early on they were Christian slaves turned into Elite troops. Later on, they became as important and disrupting as the Praetorian Guard were to the Roman Empire, basically making or breaking Sultans as they saw fit and demanding lavish treatment to boot. They were a major source of instability for centuries until they got disbanded in 1826. By then the industrial revolution was in full swing.
A last major factor that springs to mind was simply logistics. No coal was discovered in the Ottoman Empire until the 19th century.
And to some degree, it probably didn't help either that the Ottomans were at war with large swaths of Europe for the better part of its history.
Wrapping up in short:
No scientific renaissance
No capital accumulation
Sclerotic societal problems
Not friendly to Europe, where the action was happening
I'll try to give a broad answer to a broad question.
Let's start with the following question, why industrialization started in UK? Maybe the answer is in many sources, but I think that one of the best is Eric Hobsbawm (The age of revolution, the age of capital and the age of empire). The main point is that an industry requires capital (to start the venture), legal certainty (to be sure that your company will be respected by authority) and open markets (you will get a profit). This is only possible in a country with advanced institutions, low corruption and a goverment interested in the industry. Otherwise, the king/sultan/emperor of the country has to be convinced of the benefits of industrialization to promote it.
A nice example might be Christopher Columbus's voyages, where he had to find on the crown the patronage for his project. While in England, starting the industrial revolution, an industrial would be able to find several sources of patronage for his project.
Once industry is developed, you need open markets to sell your products and to buy supplies, to do this you need protection for your business (fraud, assaults, etc) and someone who can open those markets for you. Hence, here you need institutions who can garantee that trade and armies that might open new trade routes.
All these things (capital, industries, trade, armies, institutions) create a positive feedback. Which slowly is carried to other countries and imitated by others.
This progress belongs to the bourgeoisie, which will confront opposition from aristocracy, represented by the crown. That's why French Revolution (or the spring of nations) and Industrial Revolution are tied. The second needs the first one. Countries like the Otoman Empire are going to be reluctant to the industrial revolution, and they won't develop the institutions required, leaving them behind technologically. In these countries, where the crown is too strong, only industries supported by the king would prosper. Same concept applies to other european countries where the king is too strong, because while more authoritarian is a country, harder is to create the change necessary to adopt revolutionary ideas.
It so happened that scientific revolution and capitaism were introduced in Western Europe. Industrialization was a result, a consequence.
For other countries there was a choice, to follow or not. Some followed, some did not (or followed later, at various times). In the case of Turkey, on my opinion, the crucial role was played by the role of religion in the society.
I do not want to say that some religions are better than others, the important thing is how much a religion influences the society. All religions resist innovations, especially those adapted from the "infidels". In Turkey, the influence of religion was strong enough to prevent (or more precisely, to postpone substantially) following the example of the West. (Look, for example when printing press was introduced in Turkey, and why so late.)
Industrialization was postponed in other countries as well, but the time of delay varied very much. Japan, once it decided to "follow the Western ways" was able to catch in less than one generation. Same happened in Hawaii. In Turkey and Russia and China this process was very much delayed.