Imperialism was definitely one motivation behind French involvement in the War. Colonization had been ongoing for years, and Britain's imperial structure was admired (see Darwin, John, "Unfinished Empire"). However, French war aims were less about gaining new territory as they saw it, and more about making up for past losses and then-current weaknesses. In 1871, France had already lost important, mineral-rich coastal territory to Germany in the Franco-Prussian War, and fought with the Germans over Morocco. This led to a general drop in French power in the European sphere, and Germany's powerful economy did not help. Germany was more industrialized and more populous than France, and had taken steps to attempt diplomatic supremacy over the French as well via negotiation with Britain, Italy, and other European powers. The combination of previously lost territories and economic rivalry accounts in large part for France's war "aims": it wanted its land back, and wanted to regain security it had lost in the 19th century (see Clark, Christopher, "The Sleepwalkers," and Hopel, Thomas, "The French-German Borderlands").

France also had several treaties to defend that pulled it into the War, and the defense of those alliances could also be called a war "aim." One treaty was with Russia, which pledged to defend Serbia in the event of an attack. When Austria-Hungary declared war on Serbia, Russia became involved, and so in turn did France (see Mansergh, Nicholas, "The Coming of the First World War"). Another treaty was with Britain, which pledged to defend Belgian neutrality. When Germany invaded Belgium, Britain was pulled in as well, giving France another treaty obligation to uphold (Mansergh again, also see Macmillan's "The War that Ended Peace"). Upholding treaties doesn't necessarily constitute a major "aim" of France in the war the way I believe you are thinking of it, but it does account for decisions France made.

When war broke out in 1914, France didn't have any war aims. The spirit of revanche over the 'lost provinces' had been dying for a while, and Germany was France's most important economic partner. The only aim was to survive, as the Germans swept through Belgium, Luxembourg and eastern France in August, capturing the Briey Ore Fields (the center of French coal, steel, iron and industry).

By 1915, the Entente powers (Britain, France and Russia) had all agreed not to make a separate peace, and to fight until the Central Powers were defeated. This group was known as the 'Allies' after Italy joined the war on the Entente's side.

There was considerable discussion of war aims in France, with the return of Alsace-Lorraine being the key goal of the French. The map you posted shows one of the more grandiose, idealistic aims, which was to turn the clock back to 1870, undoing German unification. Popular among French Nationalists, specifically on the ultranationalist far-right, it was unrealistic, and France's political leadership knew this, for many reasons:

1. by the end of 1915, the Russians had suffered over 2 million casualties, and had been driven back into Lithuania and Belorussia. How the hell were the Allies supposed to enforce such an extensive political re-organization, when their largest member was on the backfoot, and seemed headed for major upheaval (which they experienced in 1917)?

2. Germany was the largest industrial power on the continent, and France's most important trade partner. Why the hell would they deliberately weaken them by undoing unification, when they were of much greater service to the continent (and France) unified?

3. How the HELL were the Allies, with or without Russia, supposed to enforce such a settlement? It would require millions of men, an extensive occupational authority, many of the states listed on the map (ie Hanover) did not have independent rulers that could have taken over, it would only produce huge backlash internationally and in Germany, and flew in the face of everything the Allies professed to be fighting for (rights of small nations, international law, defeat of Prussian militarism)

4. following on from point 3, the French suffered heavy losses in 1914-15, and endured the near-disaster of Verdun in 1916, followed in 1917 by the Nivelle Offensive, whose failure sparked the French Army Mutinies. The French did NOT have the manpower to enforce such a settlement, and would face considerable resistance from their Allies (Britain, Russia, USA) in trying to enforce such a settlement. It was beyond French resources, and beyond impractical.

French Aims by 1918 boiled down simply to: -Return of Alsace-Lorraine -Colonial concessions from Germany (Togoland, Kamerunland) -Concessions in the middle east (Lebanon, Syria, Cilicia) -Economic compensation from Germany -Guarantees of French security against Germany

They got Alsace-Lorraine; they got Mandates in Togoland and Kamerunland; they got Mandates in Syria & Lebanon (Cilicia was never established). This was the extent of French territorial gain

Economically, the French were in dire straits. They owed huge amounts of money to Britain and the US, the war had placed severe strain on the French state, economy and people, but the worst came in 1918. Huge swathes of French farmland had been rendered lifeless by the fighting and scorched earth (the infamous 'Zone Rouge'). But as the Germans retreated, in an act of pure spite, they poisoned wells, burned fields, flooded and booby-trapped mines, and either destroyed factories or had them packed up and shipped to Germany. This wouldn't be AS bad, had this not taken place in the territory where 64% of France's pig iron production, 24% of it's steel production, and 40% of it's coal output came from. This was disastrous, and the French were determined to get reparations for this damage. In the end, it was agreed that Germany would pay 132 billion gold marks (in reality, only 50, then 40 billion), and the Saarland, with it's factories and coal fields, would be placed under League of Nations control for 15 years, with the French controlling the resources, so as to help rebuild the economy.

Finally, for security, the French reached a compromise over the Rhineland. Some, like Marshall Foch, wanted to annex it to France; others wanted it to be made an independent buffer state; Clemenceau knew the British and Americans would agree to neither of these, and was a supporter of neither idea anyways. He got an agreement that Allied (French, Belgian and British) troops would occupy the Rhineland for 15 years, the territory itself being demilitarized, and the garrisons, already small, would be withdrawn and scaled down depending on Germany's keeping up with reparations payments. Furthermore, under the collective security of the league of nations, and via separate treaties with Britain and America, both nations would be required to intervene on France's side were Germany to attack. Germany's military was also (in theory) greatly curtailed.

Sadly, most of these would come to naught. Yes, France gained territories, but the United States did not ratify the treaty, and so did not join the League of Nations, nor would they maintain their security commitments to France. Saarland and Rhineland would return to Germany in 1935-36, under Hitler's leadership. The reparations were a thorny issue; in the end, the Germans refused to act in good faith, and when the allies ceded control of customs posts to the Germans, the payments slowed to a trickle, and this prompted the French to occupy the Ruhr in 1923, an abysmal affair to say the least. This was exacerbated by the Germans, who exacerbated their own hyperinflation crisis by hyperinflating the mark FURTHER, to avoid paying ANY reparations whatsoever! Numerous re-scheduling's and reductions would take place, until the reparations were postponed indefinitely in 1932. German 'de-militarization' is a whole other issue; suffice to say, the idea that Germany's military might had been truly curtailed by the Treaty was laughable.

The result was that France's Allies essentially abandoned it, it's economy plumbed new depths in the twenties and thirties, and Third Republic politics remained as chaotic as ever; France was set-up for failure and occupation in WWII.

TL;DR: Alsace-Lorraine, reparations and security; they got 1/3

further reading: David Stevenson, "1914-1918"; Margaret Macmillan, "Paris 1919"; Hew Strachan, "The First World War, Volume One: To Arms!"; Max Hastings, "Catastrophe"; Sally Marks, "The Myth of Reparations"; Trevor Wilson, "Myriad Faces of War"; Adam Tooze, "Wages of Destruction"

Hope that helps!