Yet, i know only french symbols of republican origins. And the "our ancestors the gauls" was part of an ideological plan to create revanchism against the germans after the franco-prussian war, which subsisted after the WWI (and a little before too, as Napoléon III tried to create a national symbol from vercingetorix). It was used to create an image of an always unified France, even in the Antiquity, by ignoring the history.
The "our ancestors the Gauls" is clearly a mark of cultural and not ideological nationalism, it may indeed have been used as part of revanchist desires against the Prussians. The history was not ignored per se, since it is proven beyond doubt that most of the "structures" of present day France, including the urban network, the population substrate and most agricultural practices were already firmly established as far back as the Antiquity. Fernaud Braudel says that many times in his series of books titled the "Identity of France".
What is are the difference between an integrationist and an assimilationist policy ? And as always, the only symbols shared by all french are republican ones, not some older than the revolution. Frenchmens identifies with the motto Liberty, equality, fraternity, even if there are different interpretations.
Integration implies a mere adherence to the country laws and institutions but not loyalty to them. Nearly all of the 7/7 bombs where integrated into the United Kingdom, in the sense that they held steady relatively well paid jobs, were involved in their local community to an extent and never openly advocated the aims they held deep inside them. Yet they were not assimilated into the British nationaly community in the sense that they held no loyalty to it. Their loyalty was directed towards their extremist beliefs not towards the nation from which their passports came from, the United Kingdom.
If France turned into a Monarchy tomorrow, I doubt that all of a sudden the vast majority of the French populace would suddenly turn its back on their loyalty towards France.
The tricolor flag is not a republican symbol at all, it was designed by the revolutionarirs but don't forget that the white in the flag represent the monarchy itself. I would even go as far as saying that blue is a colour which has always been associated to France, French heraldry always had a lot more blue than English heraldry for example.
The Gallic rooster has origins dating as far back as Gaul itself and was already associated with France during the Middle Ages.
The Marseillaise is has royalist origins and is primarily a patriotic song and not a Republican song.
The only truly Republican symbols are Marianne and the Phrygian cap, symbols rarely used outside official circles and politicians.
But the problem is that you consider France to be existent in it's modern form before the revolution. It was not. It was just different territories with different customs, tax, traditions, and languages, even religion sometimes. As you said before, in the south the Roman Law was predominant, while in the north the Common law was. The only thing that hold these territories together was the King. The revolution created the concept of a Nation-State, and created the concept of France, on ideological bases, to unify the different territories.
France was already a nation state or if you prefer a proto nation state in 1789. Differences in customs, taxation, traditions and legislative systems are not an impediment to the creation of a nation state. Despite the huge differences between England and Scotland, Britain is a nation-state, the nation state of the British people. Same for Spain with the Basque and the Catalans. Loyalty to the king was a big factor in holding these territories together, but it was not the only one. For had it been the only one, France would have collapsed at some point during the Revolutionary period.
You also seems to be forgeting that centralisation and uniformisation would have happened even if the king had stayed in power sooner or later. Indeed, Louis XVI made several attempts at reforming the system during his reign.
Institutions ? Almost all the institutions came from the revolution or the gouvernments after it. The language ? i don't see where the religion have influenced the french language, could you explain ? And culture ? Even if it has shaped the culture, there is no unified french culture. Alsatian culture is different from Breton culture, which is different from provençal culture. And for De Gaulle, yeah, the French Right always tried to link France to catholicism, but if it is so, half of Alsace in not French. And here we see why the population of musulman origin isn't integrated : the Right keep saying that the roots of France are Christians, while the Left are claiming the universalist ideals of the Revolution
The catholic church has a huge impact in allowing these institutions to be created and the modern France to take shape. Would the Enlightenment have happened in a non Christian Europe? The answer in my opinion is now. We can see that for ourselves in the light of the fact that there was no Enlightenment in either China or the Muslim world.
Many expressions in the French language are derived from biblical references, not all of them by all means but a rather large number of them. Why is this the case? Simply because for a long time the Bible was the only book read by the majority of the population. Something which is bound to have a massive impact on a language.
There is a unified French culture above the regional culture of French, taking contributions from these regional cultures and mixing them all together. A massive one is obviously French cuisine, which takes the best of what every region has to offer. Another one would literature and the like. I would also say that there is such a thing as national French character to a degree, stubborness, yearning from freedom and a certain pride would be part of it.
The roots of France are partly Christian, not entirely Christian that's for sure but Christianity played a huge part in French history and I think that's its proper to acknowledge it. The fact that France is majority Christian/Catholic does not mean non Christian/Catholic populations are not welcome, or that they should forcibly be converted. I simply think that this heritage should be acknowledged as such, especialy as there are no reasons to be ashamed of it. This is not incompatible with the principles of Laïcité at all, since acknowledgment of this heritage does not imply a state funding of christianity/catholicism at all.
In any case France has strayed away to a degree from Laïcité during the last few decades, as there is a large amount of covert funding to mosque projets and the like from municipalities. This is something whom I deplore, as we are both favouring one group over another (something inegalitarian) and straying away from our principles (something morally wrong).