In French, for expressing short, not overly disruptive agreement with words and ideas uttered during a public discourse (which is your first example), for what it’s worth, I’d probably go more with Fabrice Neyret's good answer (Oui!; Tout à fait!; C'est ça!; & Ouaaaaais!); but that’s not to say that Ikl's good answer (Bravo) wouldn’t be more appropriate for expressing over-all agreement with a just concluded speech, including a toast (which is how your second example could be interpreted).
What little I have to add beyond the two good answers already given (+1 to them both) is possibly more suitable, especially in French, for a “tête-à-tête” context than for a public one, which you correctly mention are not the same, but in English, I (being the hip dude that I mistakenly fashion myself to be) would probably be more inclined to say “Right on! or “Amen!” (with “Brother/Sister!” perhaps added in the right setting), even in a public setting than “Hear!, Hear!” (which I, perhaps just as mistakenly, find to be something that’s a tad old-fashioned [Old World?] and/or something that might be followed by a couple of “pips” and even a [Honey Nut] “Cheerio”!).
All gratuitous self-aggrandizing and fuddy-duddy-bashing aside, from these two hip alternatives to “Hear!, Hear!” in English perhaps you could arrive at:
“[En plein] Dans le mille”
in French to capture “Right-on!”/“Amen!” (cf: “bang-on/spot-on” from WordReference[dot]com);
and in the right setting you could even throw in:
“[dans le mille,] Émile”
to hold the spot of “Brother/Sister” until something better comes along.
(“(Familier) (Par plaisanterie) Renforcement plaisant de dans le mille.” from French Wiktionary)
(Note, I don't believe the speaker/toastmaster would have to be named "Emile" to use the last, rhyming suggestion, just as I believe that you could correctly and justifiably tell Papa Poule to "Relax, Max!")