I would love to know and find the truth behind this all for past and present. It seems that everything inside is very conflicted and most are from documentaries( witch I find are often biased and/or trying to push an agenda).
I've written a few things on the French Foreign Legion with deal with their development and the mythos, so I'll repost a few old things for you here. The first one here is just a broad history but hits on several points:
Mercenaries had long been a part of European Armies, and in that sense, the Legion was nothing new. France specifically had used them extensively, most notable being the Hohenlohe Regiment and the Swiss Guard. During the July 1830 Revolution though, the Swiss Guard were immediately disbanded due to close association with the overthrown regime, and the Hohenlohe Regiment was dissolved within a year as there was a law prohibiting the use of foreign mercenaries on French soil which King Louis-Philippe, the "Citizen King", was inclined to uphold.
The abandonment of these men was quite short lived though. The Legion was created in 1831 by Louis-Philippe on the advice of Marshal Soult, then Minister of War . At the time, France had just invaded Algeria and there was a great need for reinforcements. King Louis-Philippe hadn't even been king for a year at that point, so while popular, he knew that his position at the leader of France was not as secure as he might hope. The creation of a foreign legion offered him double benefits.
First off, at that time Paris was really quite overrun with foreign vagrants, many of them cast off mercenaries of the afore mentioned Swiss Guard and Hohenlohes. These men were professional soldiers, and their units being gone left them with nothing better to do other than booze, whore, and generally create a ruckus. Recruiting these men would not only get them off the streets, but also give the French a ready trained fighting force which could be shipped off to Algeria immediately.
Second, during the Bourbon years, the French Army was a mix of mercenaries and volunteers, with extra forces raised by conscription. Volunteers are not the easiest thing to rely on when you need a sudden influx of military talent, and increasing the number of troops raised via the draft is obviously a good way to lose the support from the people, which as I mentioned, was not something Louise-Phillipe could well afford at the time. So while much of the mercenary groups had been disbanded to comply with the laws governing deployment in France, this didn't preclude raising new units of foreigners to fight the foreign wars of France, with little blow back from the French citizenry should they all get killed.
So with those factors in mind, the order to create a Foreign Legion was given on March 9, 1831, and recruitment started almost immediately. In line with the implicit aim of the Legion's creation - ridding Paris of her scum - recruitment eschewed usual practices, and required no form of identification, simply accepting whatever identity the would-be legionnaire wished to offer. Aside from the veteran fighters, this very quickly resulted in criminal elements, on the run from the law, signing up. A week after the creation of the Legion, it was decided that no Frenchmen were allowed to join (excluding officers, which were French), as French authorities had already begun to attempt to force their local refuse into the Legion as a means of ridding themselves of local, French, criminals. With the policy on identification though, this was kind of a pointless prohibition, as any Frenchman desiring to join simply needed to say he was Belgian or Swiss. Aside from the alcoholic veterans, hardened criminals, and general castoffs of society, there were also a number of naive souls who joined up because they were promised land in Algeria in exchange for service.
At the time, the Legion was organized into seven Battalions based on nationality, with three of Swiss and Germans (them making up a large proportion of the traditional mercenary population in Europe at the time), one of Spaniards, one Italians, one of Belgians and Dutch, and one of Poles, and within a year or two of creation, numbered 5,000 (out of ~35,000 total French forces in Algeria in the mid-1830s). Baron Christophe Anton von Stoffle was appointed as commander of the Legion. A seasoned old Swiss soldier, he was instrumental in bringing organization to the Legion, which was, to say the least, lacking at the beginning.
The First Battalion had been shipped to Algeria in late 1831 lacking even weapons and uniforms, and the total lack of any screening process meant that not only were there plenty of criminals but a fair number of the recruits were old men or young boys, and not at all fit to fight. The French colonial authorities in Algeria were NOT happy, and the experiment seemed prone to failure from the get go, with many calling for immediate disbandment. Stoffle was a hard ass, and within the year, went a long way to turning things around. While he certainly didn't eliminate the reputation of the Legion as being the haven for thieves and cutthroats, he at least managed to turn them into a functional fighting force before he departed in mid-1832 to be replaced by Col. Michel Combe. Stoffle saw that the least qualified recruits were kicked out, and the rest cajoled into something resembling a military outfit by his collection of veteran officers and NCOs.
Over the next four years, the Legion served in Algeria and proved themselves to be a very capable fighting force, an evaluation which was nevertheless overshadowed by their enduring reputation. With the First Carlist War going on in Spain, France had obligations to uphold with the forces of the Queen Regent, Maria Christina. Rather than send French soldiers there to shed French blood for a foreign crown, the obvious answer was to sent the Legion. The leadership was not happy with the decision, and a few even officers resigned in protest, but it wasn't going to change anything, so the Legion shipped to Spain in 1835 to fight under Spanish control. It was an unmitigated disaster. While the Legion started off strong, their Battalions were split up and distributed about, and any form of support was extremely lacking. Spain saw them as last in priority for supply, and France preferred to generally forget about the Legion, meaning food, ammunition, and equipment, not to mention reinforcements, were not forthcoming. 5,000 men were sent to Spain, and some 3,600 died over the next two years - many from starvation or exposure. By the end of 1838, not even 500 men remained, and the Foreign Legion was disbanded. Or rather I should say, the First Foreign Legion was disbanded.
You see, the Legions involvement in the Carlist war was exceptionally unpopular at home in France, and continued support was a dead issue, but the idea of the Legion was not abandoned. A new ordinance in Dec. 1835 had created a second legion. Recruitment went on, and aside from a small handful sent to Spain early on, they instead were trained in France until a large enough compliment had been raised to send to Algeria at the end of 1836, eventually reaching a force of 3,500 by the end of the decade (including nearly the entire surviving compliment from the First Legion, with some 400 joining their comrades in Algeria upon disbandment. There Second Legion (or from here on out, the only Legion as they only coexisted for a few short years) performed admirably through the 1840s, and building a very deep connection with the region which became the spiritual home of the Legion, centered around their headquarters at Sidi Bel Abbès.
Over the next few decades, the Legion would continue to fill its purpose as overseas service, fighting in Crimea, Italy and Mexico. It would be in Mexico that the Legion earned one of its most enduring of battle honors, at Camerone, which still maintains an important part of Legion lore.
The Legion arrived in Mexico on March 28, 1863, part of the French intervention force sent - with initial support from the British and Spanish - to deal with Pres. Juarez's failure to follow through on interest payments for the bonds his predecessor sold to European creditors. A combined force of 7,000 Spanish, 2,500 French, and 700 (British) Royal Marines landed in late 1861, but the non-French left within a few months. With the United States preoccupied with the Civil War and unable to enforce the Monroe Doctrine, Napoleon III had much grander plans than simply recovering some money. It was clear that he wanted to actually conquer Mexico, and the other two wanted nothing to do with that so gave up on recovering the money as a lost cause, leaving only the French. And the French actually started off doing pretty poorly, losing the Battle of Puebla on May 5th, 1862 (Cinco de Mayo!), leading to further influx of troops, including, eventually, the Legion, two battalions arriving in Vera Cruz in 1863.
The Legion was given the worst job, explicitly because they were, well, Foreign. Instead of being used in a combat capacity, the French commander decided to use them for supply convoys, as the region was rife with disease, and he would prefer to see non-Frenchmen suffer.
They had been filling this job for about a month, when, the 3rd Company, 1st Battalion pulled guard duty for a convoy on April 30th. The convoy was coming from Vera Cruz, and word had reached French commanders that the Mexican Army was planning to attack it (as opposed to the usual guerrilla raiders). The detachment of 62 legionnaires and 3 officers were sent out to meet the convoy at Palo Verde and provide protection for that leg of its journey. All three of the officers were actually from different companies, as the proper officers were all ill. The one handed Capt. Danjou was chosen to take over, along with Lts. Vilain and Maudet. All three were exceptionally qualified officer, Danjou winning the Legion d'Honneur in Crimea, and the lieutenants having risen from the ranks on merit (Both were in fact Frenchmen who had joined illegally under assumed identities).
As you specifically addressed "the brutal image" of the Legion, I will add two points to what has already been written. I am mainly addressing the time until the end of the 1950s and the colonial wars of the legion.
Firstly, the brutal image was a reflection of life in the legion. Discipline was harsh and included corporal punishment long after it was abolished in the major European armies. Depending on the officers, the punishment was sometimes arbitrary and quite savage. Another factor was the nature of the wars it fought. Colonial Wars had a tendency towards excessive violence like killing/decapitation of prisoners and the mutilation of their bodies. To use a modern day analogy, colonial wars at their worst were like ISIS fighting ISIS. The stories of exotism and violence were a popular topic at the time and accordingly such accounts from legionnaires were frequently covered by the press or published as books. Even though these accounts were often exaggerated in one way or another, there wasn't much need in doing so.
Secondly, this brutal reality comfortably matched the legions' mythology already described here, as it was just too tempting to portray legionnaires as criminals or psychopaths doing horrible things or romantic heroes suffering in a foreign land. The problem is, that up to this day, the origins and motivations of the legionnaires are not thoroughly investigated. The evidence I know of, however, suggests that joining the legion was, broadly speaking, a specific form of working migration of poor and jobless workers. A case study on legionnaires from Switzerland supports this view and highlights the relatively high number of orphans among the recruits.
To put it short: While brutal image of the legion for its colonial time is somehow exaggerated but basically based on reality, this is not the case for the image if the legionnaires. While the presence of adventurers, weirdos and criminals in the legion is well documented, they most likely only represent a tiny yet colourful minority.
As a side note, most of it holds true for the Spanish foreign legion as well, founded after the French paragon in 1920.
Sources, sadly only in German:
Koller, Christian: Kriminelle Romantiker in der exotischen Hölle. Zur transnationalen Medialisierung der französischen Fremdenlegion, Saeculum 62,2 (2012), 247–266.
Koller, Christian: Die Fremdenlegion. Kolonialismus, Söldnertum, Gewalt, 1831–1962, Paderborn 2013.
Huber, Peter: Fluchtpunkt Fremdenlegion. Schweizer im Indochina- und im Algerienkrieg, 1945–1962, Zürich 2016.