How strict is the 'nothing biblical' rule? Does it rule out Isabel and Isabella as variants of Elizabeth and Jack as a variant of John for example?
James Francis would be lovely but is biblical.
Patrick, Edmund, Oliver, Max, Magnus, Alistair, Laurence, Walter, Fabian, Robert?
Eleanor Frances is lovely, but as a PP pointed out - Eleanor of Aquitaine was a former queen consort of England in the 1100s. There was also the Eleanor (of Castille?) the queen consort for whom the Eleanor crosses were made.
How about Clarissa, Juliet, Sabrina, Seraphina, Georgina, Margot, Verity, Laura? Or a rose name - Rosanna, Rosalind, Rosamund, Rosemary?