They were similar to an extent. Both the Franks and Anglo-Saxons were originally Pagan, and worshiped pretty much the same gods, although very little is actually known about their original pagan religious beliefs as we only have scant literary accounts and a very limited number of runic inscriptions.

Both the Franks and Anglo-Saxons originally used the Elder Futhark Runic system, however we have a very limited number of runic inscriptions from either Proto-English/Anglo-Frisian and Proto/Old Frankish. As far as I know only two runic inscriptions have been identified as definitively Frankish, and even its later forms are extremely poorly attested. Old Low Franconian, a language derived from Old Frankish was a considerable influence on Old High German, however OHG is more of an umbrella term for a number of dialect clusters derived from different Germanic languages. Anglo-Frisian Runes are attested in about 100 objects, including those found in England and in Frisia. Unlike on the continent, runes continued to be used after the conversion to Christianity. Given that the dialects that gave rise to Old English were in very close proximity to the same areas that Proto-Norse originated, there is some ambiguity as to which language early Runic inscriptions from Denmark belong to. Keep in mind, I am largely talking about roughly 150 to 600 AD here.

We do know that some of the early cemetaries in Anglo-Saxon England have Scandinvian influences, and it is likely some "Anglo-Saxons" migrated from Southern Sweden and Denmark, and there was more than likely a cultural and dialect continuum between Old English and Proto-Norse in the earliest period of Anglo-Saxon settlement, however this could be explained by Anglo-Saxons importing objects from Scandinavia.

The Franks and Anglo-Saxons were living in very close proximity to each other in parts of Germany and the Netherlands, and it has been theorized that at least some Franks migrated to England with the Anglo-Saxons, and we know that there was trade with the Franks at the same time of the Anglo-Saxon migration to England.

In terms of an affinity for each other, who knows. The pre-migration period and migration period history of Germanic tribes is not well understood, as we generally lack inscriptions and literary accounts vital to our understanding of culture. The archeological cultures of these two groups can be very distinct from one another, although I'm certainly not an archeologist. I'm sure that there were alliances made and wars fought between Franks and Anglo-Saxons at some point. We do know that Saxons and Franks served as Foederati in the Roman Military, and I believe that is likely that there were Germanic tribesmen already stationed and settled in Britain during the last days of the Western Roman Empire, and probably invited over more of their fellow tribesmen to Britain during and after the Roman evacuation of Britain around 410 AD. After a great deal of Anglo-Saxons left the continent to settle in Britain, the Franks continued to migrate southwards in what is now Germany and France spreading their language and their culture became quiet distinct. Over time the Frankish language split into numerous languages, most notably Old Franconian splitting into Low Franconian and West Central German, creating Old Dutch and Old High German. The Franks eventually began speaking Gallo-Romance, although it would incorrect to label this as French because the 8th century is long before French and other Gallo-Romance languages became distinct languages. The French language derived it's name from the Franks, and adopted a huge amount of Frankish loanwords. French was just one of many Gallo-Romance languages including French, Picard, Gallo, Angevin, and Norman, all distinct languages, however Norman was perhaps the most different including grammatical differences and considerably different vocabulary on a basic level. None of these languages were standardized, and many of the old Gallo-Romance languages have gone extinct due to the spread of the French language which was mainly limited to the areas surrounding Paris during the middle ages.

Old English was also not necessarily a standardized language in that it had four main dialects, Kentish, Mercian, Northumbrian, and West Saxon. Most of the legal documents and texts that survive were written in Old West Saxon, however it was not necessarily spoken by a majority of Anglo-Saxons. The different dialects had differences in grammar, vocabulary, and pronunciation. The different areas were settled at different times, and had different origins on the continent.

Any how, we just don't really have the evidence to answer your question because pretty much all we know about the Franks and early Anglo-Saxons is from archeology and scant or vague literary sources.