General use:
* Formellement: This is the most direct translation and works in most situations.
* De manière formelle: This translates to "in a formal manner" and is a bit more descriptive.
Specific contexts:
* Officiellement: This means "officially" and is used when referring to something done according to established rules or procedures.
* Solennellement: This translates to "solemnly" and is used for events or occasions that are very serious and dignified.
* Rigoureusement: This means "rigorously" and is used when describing something done with strict adherence to rules or standards.
Examples:
* Il faut s'habiller formellement pour le gala. (You must dress formally for the gala.)
* Le procès-verbal a été rédigé de manière formelle. (The minutes were written in a formal manner.)
* L'accord a été signé officiellement. (The agreement was signed officially.)
* La cérémonie a été solennellement célébrée. (The ceremony was solemnly celebrated.)
* Le travail a été effectué rigoureusement. (The work was done rigorously.)
The best choice for you will depend on the specific context of what you are trying to say.