First given name from birth search of daughter on New Zealand BDM website in June 2020:
1850/2118. French, Eleanor. Mother: Ann. Father: John

Arrived in New Zealand on the ‘William Bryan’ with husband John French, and daughter Mary Ann French. The ‘William Bryan’ sailed from Plymouth, England on the 19th November 1840 and arrived at New Plymouth, New Zealand on the 30th March 1841. The passenger list shows steerage passengers:
French, John 28 Agricultural Labourer
“ Ann [Wife]
“ Mary Ann [Girl]

Result from birth search in June 2020 for children born in New Zealand on NZ BDM website:
1853/1265. French, Sarah. Mother: Ann. Father: John
1848/632. French, Jane. Mother: Ann. Father: John
1850/2118. French, Eleanor. Mother: Ann. Father: John
1857/4133. French, Susan. Mother: Ann. Father: John
1859/5274. French, Emma. Mother: Ann. Father: John
1855/3096. French, George. Mother: Ann. Father: John