I agree with post #6, but would add that Louis-Philippe's monarchy was plagued by protests from emerging radicals on the left and conservatives on the right. As a response, his regime, while devoted to the juste milieu, lurched far to the right as it faced the profound social problems of 19th century France. In the end, it was a very short-lived coalition between leftists like Louis Blanc and liberal bourgeoisie that brought about the downfall of the king after he suppressed public demonstrations against his rule. But this coalition quickly fell apart after Louis-Philippe abdicated. The brutal fighting in Paris between radical democrats and socialists on the one side, and soldiers of the bourgeois National Assembly on the other, called the "June Days" and famously interpreted by Marx as a (failed) class revolution demonstrated the serious divisions in French society during this period. To answer your question fully, ultimately I think Louis Napoleon, who eventually emerged from the chaos as president and later emperor, was able to channel a lot of liberal, even radical elements into his presidency, which enacted fundamental reforms while certainly adopting a conservative approach to power.
This is the kind of question that could be more easily answered after doing some research. An excellent place to begin doing research is Google Books. (For some reason, Google does not make the "Books" tab very visible; you can find it by clicking on the "more" tab.) For instance, here is what I found when I typed "conservatives in France 1825-1848":
Here's what I found when I searched for "liberals in France 1825-1848:
Google Books is often far more helpful than a simple Google search, because many of the books listed and previewed in GB are peer-reviewed. In other words, experts have often vouched for their reliability.
Good luck with your work!
In addition to using Google Books as a way of researching this topic (as I suggested in another post), you may also want to take advantage of your school library, especially if that library has two things: (1) access to some useful databases, and (2) a librarian willing to help. Most librarians are indeed more than willing to help students in search of information, and no student should be reluctant to ask a librarian for assistance. Most librarians have years of experience in helping people find information, and most of them genuinely enjoy helping others. Since we rely so much on the internet today, we often forget about librarians, but often they are among the most internet-savvy people around!
I would say that the conservatives were more influential in general than the liberals. During the time period you are talking about, there was little or no time in which the liberals were really in control of the government.
Of course, the conservatives did not have it all their own way. You had things like the overthrow of Charles X that represented wins for the liberals. However, it seems like these things always gave way to conservatives retaking power. Even the Revolution of 1848 led only to the rise of Louis Napoleon. So all in all, it seems clear that the liberals were influential, but they were never able to translate their influence into an actual chance to rule.
What I would recommend that you do to help you organise your information is to look at the information you have already got and break it down into smaller topics, attaching the information you have to one of these topics. When you have done that, then you can try to work out the relationship and the links between these topics. Steps like this can often help us to understand complex information.
Another source of information is asking your tutor to recommend specific books. As he/she will be marking your assignment, that will clearly help you to focus on the sources that he/she thinks are important. It also shows great initiative.
The liberal intervention of Louis Philippe d'Orléans into the reign of conservative Charles X through the occurrence of the July Monarchy (1830), also called the Three Glorious Days, indicates that liberalism and radicalism dominated to a significant extent. Louis Philippe's constitutional monarchy sought what he called a just middle ("uste milieu") where royal abuse and excesses were rejected and popular extremes and excesses were equally rejected.
I think that you will also find this web site helpful.
My first thought when I read your question is that much of French politics at that time would still be influenced by the aftermath of the French Revolution and Napoleon.