While the Algerian's have close ties with France, they are looking at the "Bang for your Buck" principle. Obviously they've not priced it as nicely as the Algerian's would have liked, IF, they've definitively been "non-down selected".
Since Algeria's neighbour Libya has been welcomed back into the global community, I think that there's a need for countries on the North African coast to start to replace their outdated Russian technology. They see the West as a "more appropriate" option, as buying Arms from the UK / US shows certain alignment with Western philosophies.
Algeria has need to update her fleet, which I'm led to believe, contains a few vessels that are more than 40 years old. In addition if you look at her coast line, the waterfront onto the med is over 700 miles long !!
Looking at the Type-23 hull, Algeria has obviously seen how successful these have been for both the UK & Chile. I don't doubt they would love to have a few 2nd hand ships, but that isn't gonna happen any time soon, so it's probable that they're looking for the Hull form / Platform, but not necessarily the Weapons fit.
That aside, I'm sure if the deal is correct, they'd take what BAE is offering, including specific systems / equipment (Radars, Missiles, etc), support through life / spares & additional ship hulls (including maybe an oiler, an LSD(A), an LPD, or even a few F2000 derivative type hulls, who knows ??).
Phased over say 10 year period, they could build a comfortable sized navy, with adequate support ships, capable of protecting their EEZ & coastline.
Now that's progress !!
SA