An important problem (that could virtually be said of everything we know about the Early Middle Ages) is that we only get the clerical perspective. This is always something to be taken into account, but this is especially important when we analyse things like mythology—can we rely on monks and bishops to give an accurate report of lay traditions? (short answer: no)

Gregory of Tours (writing in the 580s?), in his Ten Books of History (book II), gives a verisimilar (if certainly wrong) account of Frankish migration. It has been suggested that, not unlike Jordanes' similar (though longer) tale about the Goths, these migrations stories were the result of a Roman outlook: barbarian people, especially Germans, were supposed to wander about, even when (like the Franks) they had in fact been sedentary for hundreds of years. But it seems that a century after the conquest of Gaul, Gregory thought that the Franks originally came from Pannonia (Hungary), went to Thuringia (central Germany) and eventually migrated to the Rhine. This account may reflect a process of accommodation of various origin stories (this type of conflation is quite typical of oral transmission: some members of Clovis' army probably were Huns (coming from Pannonia); it has been hypothesised (by Edward James, if I recall correctly) that the Merovingians may have been a Thuringian family; but the homeland of the Franks was the Rhine Valley.

The Ps.-Fredegar (writing in the 650s?), an anonymous author, did not shy away from mythological accounts (esp. in his book III). One of them, the famous tale of the four beasts (Clovis' father, he said, saw on his wedding night several animals that epitomised the decay of the Merovingian line—and here another problem becomes obvious with the handling of “Fredegar” material: it is quite hostile to the Merovingians), is no more than a scholarly creation, inspired by the biblical Book of Daniel. Two other elements, on the other hand, could be interpreted as origin myths. The first one is that the mother of Merovech (Clovis' alleged grandfather) was impregnated by a sea monster, the “Quinotaur.” It has long been trendy to interpret this as a reworking of a pagan legend; but it is questionable whether it is not actually a covert slander of adulterous queens (which may have been based on an actual legendary pattern, and then twisted to fit Fredegar's end). It may also have been no more than an etymological gloss on Merovech's name.

The second one is that the Frankish people was actually founded by Trojan exiles. This time, the account is not hostile (because the author probably self-identified as a Frank—it was kings he criticised), but it is also painfully obvious that it is a Roman creation, and not “indigenous”. That being said, it could be quite old: we know that by the end of the 4th century, Romans thought that they shared a common origin with Burgundians; though the source of this information (Ammianus Marcellinus) did not precise how and why, it is possible that the genealogical link underlying this connection was Trojan descent. It is clear that Roman diplomacy “offered” this kind of hugely symbolic but costless myths to barbarian people to foster valued alliances; it is not impossible that the Burgundians were not the only one to benefit from this Roman reworking of their national history (equally possible is the idea that the Franks, which lived in a more backward area until the 6th century, later copied this idea). In any case, this tale would prove very successful: many later authors would elaborate and add details on top of it, and it was still believed in 18th century France.

tl;dr: myths of Frankish origins we have are probably genuine, but they were written and created from an essentially Roman/post-conquest perspective. Myths of Merovingian origin are particularly dubious.

On top of the sources, if you can find them, here is a short (and certainly incomplete—I am pretty sure that I have forgotten an important article by Wood) bibliography (the issue of sacral kingship is directly linked with Fredegar's myths, hence the density of articles on this theme):

• Ian Wood, The Merovingian Kingdoms (1994) (reference work; it includes a discussion of Frankish origins, especially relevant to my first point)

• —, “Defining the Franks: Frankish origins in Early Medieval Historiography”, in S. Forde et al., Concepts of National Identity in the Middle Ages (1995)

• Edward James, The Franks (1991) (reference work; see Wood 1994)

• Alexandre C. Murray, “Fredegar, Merovech and Sacral Kingship” in Walter A. Goffart et al., After Rome's Fall (1998) (with special mention to Fredegar's account of Merovech's birth, and additional material on Carolingian views of the Merovingians. Other good articles in this book, esp. Susan Reynold on migration accounts)

• Erik Gooseman, “The long-haired kings of the Franks: 'like so many Samsons?'”, Early Medieval Europe (2012) (begins with a short review on the changing views about Merovingian kingship, which points to several other articles)

• Régine le Jan, “La sacralité de la royauté mérovingienne”, Annales (2003) (if you can read French, an exhaustive exposition of the traditional view)

• Walter Goffart, “The Fredegar Problem Reconsidered”, Speculum (1963) (important and seminal article on Fredegar; it was reedited, if I recall correctly, in Goffart's The Long-Haired Kings)