You asked whether there is a street in Venice called *dei Franceschi*, and a Defranceschi bridge in Rijeka. There is a street, and it is better than expected. There is no bridge — there is something bigger.
Venice — Rio Terà dei Franceschi, at Santi Apostoli
It exists, it is in Cannaregio, and Giuseppe Tassini — whose Curiosità veneziane of 1872 is still the authority on where Venetian street names come from — explains it in full.
«FRANCESCHI (Rio terrà dei) a' SS. Apostoli. La denominazione di questo Rivo, il quale, prima del suo interramento, era attraversato da un piccolo ponte, pur esso detto dei Franceschi, ricorda quella famiglia cittadinesca Franceschi, la quale faceva per arma un leone rampante col motto: Sero sapimus.»
The name of this rio — which, before it was filled in, was crossed by a small bridge also called dei Franceschi — recalls that citizen family Franceschi, whose arms were a lion rampant with the motto «Sero sapimus»: we grow wise too late.
So there was a Ponte dei Franceschi in Venice, and the street is what is left of it after the canal was filled.
And it is named for a man this site already has
Tassini goes on. A Benda of this family presented, at the redecima of 1514, the schedule of her many goods, among them buildings in the contrada of Santi Apostoli. And «anche Andrea Franceschi, Cancellier Grande, nipote ed uno degli eredi di essa Benda, notificò nel 1537 di possedere una casa da statio a S. Apostolo» — Andrea Franceschi, Grand Chancellor, nephew and one of Benda's heirs, declared in 1537 that he owned a casa da statio at S. Apostolo.
That is the Andrea already on this site — Titian's friend, Grand Chancellor of the Republic. The street is named for his family's houses. Not our kin, and this archive has never claimed him; but the question «is there a street in Venice called dei Franceschi» turns out to have the same answer as «who is the man in the Titian».
Four things about Andrea that this archive did not have
Tassini's entry is the fullest short life of him anywhere. He was born in 1472 — the site has said 1473 — and died in 1551. He was the son of Piero Franceschi, zogelier — a jeweller — son of the late Bortolo dalla seda, of the silk trade. So the Grand Chancellor of Venice was a jeweller's son and a silk merchant's grandson, which is what cittadini originari actually means in practice.
In 1513 he travelled to Constantinople and to Cairo with the Republic's ambassadors. He was for about seven years librarian of the Marciana. He was learned in Greek and Latin, a lover of music, and a collector of medals. Titian portrayed him twice.
The Cairo journey needs a note. This archive earlier cleared a study of the Venetian embassy to Cairo of 1512 as irrelevant, on the ground that its Andrea de' Franceschi was of Cividale di Belluno and a different family. Tassini puts this Andrea on that road in 1513. One of the two readings is wrong and it may be ours. Reopened.
Three more Venetian vignettes, from the same book
1560 — a Ferigo Franceschi declares that he owns two-thirds of a house at San Nicolò, under a roof called la Cha Matta.
1575 — the terrible plague of that year broke out in the parish of San Marziale in the house of a Vincenzo Franceschi, where a man from Trento, already infected, had been given lodging. Tassini reports it without comment; it is the sort of sentence a family would rather not find in a street-name dictionary.
1586 — Angelo di Franceschi, son of Girolamo, secretary of the Senate, was murdered by Carlo Zeno, who also fired an arquebus at his brother-in-law in the palace at the Frari, and was beheaded on 29 March 1586.
Rijeka — not a bridge, a pier
There is no Defranceschi bridge in Rijeka, and this archive looked hard for one. There is a De Franceschi pier — «De Franceschijev gat», in the main harbour, and it is one of the more important pieces of ground in the city.
It was built as the Mol Zichy, named for the Hungarian counts, and it is on the Croatian maritime-heritage register as «Pristanište Zichy / De Francescijev gat»: 150 metres along the east side, 134 on the west, 80 across the south, about six metres of water at the edge.
Two things happened on it. In 1882 the first building in Rijeka harbour to be constructed in iron and concrete — warehouse 4, designed 1881 — went up on this pier, probably to the design of the architect Mate Glavan. And on 30 August, in the first years of electric light, Károly Zipernowsky — the inventor of the transformer, with Bláthy and Déri — lit Gat Zichy and warehouses II and III with four lamps borrowed from the Torpedo Factory. Two bulbs in the warehouse, two on the pier. The first electric light in Rijeka was switched on standing on the De Franceschi pier.
And nobody says which De Franceschi
The heritage register gives the pier both names and no explanation. Rijeka renamed a great many Hungarian and Italian things after 1945, and the obvious candidates are all in this archive — Carlo the historian, whose family Kobler traced in the Fiume registers; Ivan Defranceski, political commissar in the Istrian partisans in 1943–45; or one of Kobler's three Fiume households of the name. This archive will not guess. The Rijeka city archive and the municipal street-naming records would settle it in an afternoon, and it is on the list.
Any others?
Those are the two this archive can document. Against them stand the things that are not landmarks of this name and get mistaken for them: the Villa De Franceschi at Seget near Umag, which is a house and this family's own; the Stanzia De Franceschi at Svetvinčenat, a farmstead that had already passed out of the family by 1820 and survives only as a cadastral name; and, in Carnia, the ordinary fact that half the graveyard at Gorto carries it. If you know of another — a school, a square, a ship — this archive would rather chase it than assume it does not exist.
Venice: Giuseppe Tassini, «Curiosità veneziane, ovvero Origini delle denominazioni stradali di Venezia» (Venice, 1872 edition), the entry FRANCESCHI (Rio terrà dei), pp. 288–289, read from the Internet Archive scan; his own authorities are the «Cronaca di quarantasei famiglie di Cittadini Veneziani» (Biblioteca Marciana, Cl. VII, Cod. CCCXLI) and the «Memorie concernenti la Vita dei Veneti Cancellieri Grandi» (Cl. VII, Cod. CLXVI). Rijeka: the Croatian maritime-heritage register entry «Pristanište Zichy / De Francescijev gat»; and the Rijeka chronology at moja-rijeka.eu, citing Nana Palinić, «Povijesna skladišta riječke luke», in «Industrijska baština» I (2003), Pro torpedo, Rijeka 2005, p. 395.