Allez les bleus ! already suggested by cl-r in a comment is common when supporting a national team but is only used when a sport team is involved.

For other kinds of patriotic rallies, singing the Marseillaise would be the usual way to show support.

One can say “Allez les Bleus !” but a lot of people think they are saying “Aller les Bleus !”; this last spelling (on banners for instance) is not correct (ref.).

It is also possible to say “Allez les bleus, allez la France” (ref.). Of course you can also write “Allez la France !” on banners and say it too (ref.).

For a three syllable (like “U-S-A!”) patriotic exclamation, there’s “Vive La France!” but, as mentioned in lawless.com‘s entry for that expression:

You probably won’t hear the patriotic exclamation Vive la France !
more than a few times a year [as] it tends to be reserved for occasions
like Bastille Day, French elections, international sports, and, sadly,
national tragedy.(the “French elections” link to youtube was also found in that same lawless.com entry)

Please note, however, that in addition to lawless.com‘s caution about “probably [not hearing] … ‘Vive la France!’ more than a few times a year,” I would also caution that the following videos that I found of people repeatedly chanting these three syllables in organized unison (as is done with “U-S-A!”) were not filmed in France, which could mean that this staccato/repetitive/in unison use of “Vive La France! Vive La France! Vive La France!” is a “non-French-native” way of paying homage to and showing solidarity with France (and not one that is typically used in France by French natives):

General de Gaulle in Mexico (where at the very beginning it sounds to me like the crowd is chanting “Vive la France!”) (from britishpathe.com)

Solidarity with France shown in London following the November 2015 Paris attacks (posted by guardianwitness on youtube)