Innerhofer, the 2014 Olympic silver medallist and 2011 super-G world champion, clocked a time of one minute 48.45 seconds down Courchevel's L'Eclipse piste with Crawford 0.31 slower.
Switzerland's Alexis Monney (23) was third fastest, 0.34 off Innerhofer's time.
Reigning world champion Vincent Kriechmayr (31) of Austria was one of several who decided to take a day out ahead of Sunday's race.
Other non-starters included Norway's super-G silver medallist and downhill favourite Aleksander Aamodt Kilde (30) and Switzerland's Marco Odermatt (25).
Kilde was fastest in Wednesday's first training, with Innerhofer second.
Italy's Dominik Paris (33), recovering from his big fall in Thursday's super-G, was back in action and fifth fastest with compatriot Florian Schieder (27) sixth in Friday's training.
A third session is scheduled for Saturday.
Favourite Goggia fastest in third women's training
Favourite Sofia Goggia (30) was fastest for Italy in third training for Saturday's downhill at the Alpine skiing world championships in Meribel.
The 2018 Olympic champion and 2022 silver medallist clocked a best time of one minute and 28.31 seconds down the Roc de Fer piste in sunny conditions, 0.46 faster than Austria's Mirjam Puchner (30).
Norway's Kajsa Vickhoff Lie (24) was third with teammate Ragnhild Mowinckel (30) fourth and Switzerland's Lara Gut-Behrami (31), the reigning Olympic super-G champion, fifth.
Reigning world champion Corinne Suter (28) of Switzerland was only 23rd.
Italy is going for a third women's gold in three events so far at the French resort, with Federica Brignone (32) winning the combined on Monday and Marta Bassino (26) the super-G on Wednesday.
Goggia is also looking to complete her personal set of championship medals after taking silver in super-G in 2019 and bronze in the giant slalom in 2017.
American Mikaela Shiffrin (27), who took her 12th career world championship medal with silver in the super-G, is not racing the downhill.
